new york state common core 6-8 mathematics curriculum
TRANSCRIPT
Fluency Support for Grades 6β8 Date: 4/2/15
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6-8 G R A D E
New York State Common Core
Mathematics Curriculum
Table of Contents
Fluency Support for Grades 6β8 Introduction ..................................................................................................................................................... 3
Fluency Expectations............................................................................................................................ 3
Rapid White Board Exchanges .............................................................................................................. 5
Sprints ................................................................................................................................................. 5
Sprint Delivery Script ............................................................................................................................ 6
Mapping of Fluency Exercises to Fluency Requirements .................................................................................. 8
Grade 6 Fluency Exercises
SprintβMultiplication of Fractions I ....................................................................................................15
SprintβMultiplication of Fractions II ...................................................................................................19
SprintβDivision of Fractions I .............................................................................................................23
SprintβDivision of Fractions II ............................................................................................................27
RWBEβLong Division Algorithm .........................................................................................................31
RWBEβAddition of Decimals I ............................................................................................................32
RWBEβAddition of Decimals II ...........................................................................................................33
SprintβAddition of Decimals I.............................................................................................................34
SprintβAddition of Decimals II ............................................................................................................38
RWBEβSubtraction of Decimals .........................................................................................................42
SprintβSubtraction of Decimals ..........................................................................................................43
RWBEβMultiplication of Decimals ......................................................................................................47
SprintβMultiplication of Decimals I ....................................................................................................48
SprintβMultiplication of Decimals II ...................................................................................................52
SprintβGreatest Common Factor .......................................................................................................56
SprintβRational Numbers: Inequality Statements ..............................................................................60
SprintβAddition and Subtraction of Equations ...................................................................................64
RWBEβMultiplication and Division of Equations with Fractions ..........................................................68
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RWBEβArea of Shapes .......................................................................................................................70
Grade 7 Fluency Exercises
SprintβInteger Addition .....................................................................................................................73
SprintβInteger Subtraction.................................................................................................................77
SprintβInteger Multiplication .............................................................................................................81
SprintβInteger Division ......................................................................................................................85
SprintβGenerating Equivalent Expressions .........................................................................................89
SprintβEquations ...............................................................................................................................93
SprintβInequalities.............................................................................................................................96
SprintβFractions, Decimals, and Percents...........................................................................................99
SprintβPart, Whole, or Percent ........................................................................................................103
SprintβPercent More or Less ............................................................................................................107
SprintβFractional Percents ...............................................................................................................111
Grade 8 Fluency Exercises
Sprintβ Properties of Integer Exponents to Generate Equivalent Expressions I .................................115
SprintβProperties of Integer Exponents to Generate Equivalent Expressions II .................................119
RWBEβOperations with Numbers Expressed in Scientific Notation I .................................................123
RWBEβOperations with Numbers Expressed in Scientific Notation II ................................................124
RWBEβMultistep Equations I ...........................................................................................................125
RWBEβMultistep Equations II ..........................................................................................................126
RWBEβMultistep Equations III .........................................................................................................127
RWBEβArea and Volume I................................................................................................................128
RWBEβArea and Volume II ...............................................................................................................130
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Fluency Support for Grades 6β8
INTRODUCTION The Common Core Standards for Mathematics call for students to obtain and demonstrate not only conceptual understanding and problem solving, but also procedural skill and fluency. Documents released by Student Achievement Partners go on to describe procedural skill and fluency as speed and accuracy in calculation that enable students to apply mental resources to more complex concepts and processes.
Standards in grades K-6 use the word fluent, or fluently, to explicitly call for students to achieve quickness and accuracy in calculations. In later grades the standards themselves do not use the word fluent or fluently. By middle school, fluency is less about calculation, and more about ease of manipulation of expressions, equations, notations, etc. Thus fluency exercises are applied toward any skill needed to manipulate expressions and equations with ease. For example, in Grade 8 students should work towards quickly and accurately solving general, one-variable linear equations.
An additional resource for guiding fluency work in later grades is the PARCC Model Content Frameworks for Mathematics. This document provides a section entitled, Key Fluencies and Examples of Culminating Standards. The table below lists the standards identified therein for Grades 6-8, along with the accompanying narrative from the document.
PARCC Model Content Frameworks for Mathematics1 β
Fluency Expectations or Examples of Culminating Standards for Grades 6β8
6.NS.2 Students fluently divide multi-digit numbers using the standard algorithm. This is the culminating standard for several
yearsβ worth of work with division of whole numbers.
6.NS.3 Students fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each
operation. This is the culminating standard for several yearsβ worth of work relating to the domains of Number and
Operations in Base Ten, Operations and Algebraic Thinking, and Number and OperationsβFractions.
6.NS.1 Students interpret and compute quotients of fractions and solve word problems involving division of fractions by
fractions. This completes the extension of operations to fractions.
7.EE.3 Students solve multistep problems posed with positive and negative rational numbers in any form (whole numbers,
fractions, and decimals), using tools strategically. This work is the culmination of many progressions of learning in
arithmetic, problem solving and mathematical practices.
7.EE.4 In solving word problems leading to one-variable equations of the form ππ₯ + π = π and π(π₯ + π) = π, students solve
the equations fluently. This will require fluency with rational number arithmetic (7.NS.1β3), as well as fluency to some
extent with applying properties operations to rewrite linear expressions with rational coefficients (7.EE.1).
1 The PARCC Model Content Frameworks for Mathematics can be found at http://parcconline.org/mcf/mathematics/overview-parcc-model-content-frameworks-mathematics
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7.NS.1-2
Adding, subtracting, multiplying, and dividing rational numbers is the culmination of numerical work with the four
basic operations. The number system will continue to develop in grade 8, expanding to become the real numbers by
the introduction of irrational numbers, and will develop further in high school, expanding to become the complex
numbers with the introduction of imaginary numbers. Because there are no specific standards for rational number
arithmetic in later grades and because so much other work in Grade 7 depends on rational number arithmetic (see
below), fluency with rational number arithmetic should be the goal in Grade 7.
8.EE.7
Students have been working informally with one-variable linear equations since as early as kindergarten. This
important line of development culminates in Grade 8 with the solution of general one-variable linear equations,
including cases with infinitely many solutions or no solutions as well as cases requiring algebraic manipulation using
properties of operations. Coefficients and constants in these equations may be any rational numbers.
8.G.9
When students learn to solve problems involving volumes of cones, cylinders, and spheresβtogether with their
previous Grade 7 work in angle measure, area, surface area and volume (7.G.4β6)βthey will have acquired a well-
developed set of geometric measurement skills. These skills, along with proportional reasoning (7.RP) and multistep
numerical problem solving (7.EE.3), can be combined and used in flexible ways as part of modeling during high
schoolβnot to mention after high school for college and careers.19
Development of fluency for any skill, computational or otherwise, is achieved optimally through exercises that create excitement through use of time constraints or time-related goals. Note, however, that fluency exercises are not a means for learning the skill for the first time, rather fluency exercises are to be conducted after the delivery of one or several lessons which develop conceptual understanding and which provide opportunities to practice newly learned skills in a non-time-constrained setting. Students must first understand why the procedures or processes they are using work and must achieve a general capacity in that skill before they are ready to work on quick accuracy.
A second critical element in an effective fluency exercise is providing students with immediate feedback to the correctness of their work and to their progress in developing speed.
This document provides fluency exercises of two types, the Rapid White Board Exchange (RWBE) and the Sprint. The RWBE allows time for students to share their work with a partner, to remediate small learning gaps, and for the teacher to assess each studentβs readiness for further fluency work on that skill. The RWBE supports a class of students in moving towards readiness for fluency, while allowing those students who are ready, to begin the work of fluency. Thus, the RWBE should be used before a Sprint on a given skill. Additionally, the RWBE is a practical tool for students to utilize when practicing skills that require more written support or work space.
While Sprints are not useful for skills that require significant work space, they are immensely effective at improving fluency for skills requiring little written support. For example, a Sprint is not practical for practicing the long division algorithm, but is practical for multiplication of integers which can be computed mentally. Sprints on a given skill should always be administered as a back-to-back pair of coordinated Sprints on the same skill. There is a designated period of time between the two Sprints where students can work at a slower pace, asking questions and getting assistance if needed.
This document provides RWBEβs and Sprints to support each of the fluencies identified in the Standards and the PARCC Model Content Framework. It is not recommended that fluency work be restricted to the module(s) in which a given skill is introduced. Rather, teachers are encouraged to work on fluencies throughout the year, once conceptual understanding has been established. Reusing the same fluency
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exercise as often as once every two weeks is a reasonable and appropriate means of developing and improving fluency on a given skill.
Rapid White Board Exchanges Implementing an RWBE requires that each student be provided with a personal white board, a white board marker, and an eraser. An economic choice for these materials is to place two sheets of tag board (recommended) or cardstock, one red and one white, into a sheet protector. The white side is the βpaperβ side that students write on. The red side is the βsignalβ side, which can be used for students to indicate they have finished workingββShow red when ready.β Sheets of felt cut into small squares can be used as erasers.
An RWBE consists of a sequence of 10 to 20 problems on a specific topic or skill that starts out with a relatively simple problem and progressively gets more difficult. The teacher should prepare the problems in a way that allows the teacher to reveal them to the class one at a time. A flip chart or PowerPoint presentation can be used, or the teacher can write the problems on the board and either cover some with paper or simply write only one problem on the board at a time.
The teacher reveals, and possibly reads aloud, the first problem in the list and announces, βGo.β Students work the problem on their personal white boards as quickly as possible. Depending on teacher preference, students can be directed to hold their work up for their teacher to see their answers as soon as they have the answer ready or to turn their white boards face down to show the red side when they have finished. In the latter case, the teacher says, βHold up your work,β once all students have finished. The teacher gives immediate feedback to each student, pointing and/or making eye contact with the student and responding with an affirmation for correct work, such as βGood job!β, βYes!β, or βCorrect!β, or responding with guidance for incorrect work such as βLook again,β βTry again,β βCheck your work,β etc. Feedback can also be more specific, such as βWatch your division facts,β or βError in your calculation.β
If many students have struggled to get the answer correct, go through the solution of that problem as a class before moving on to the next problem in the sequence. Fluency in the skill has been established when the class is able to go through a sequence of problems leading up to and including the level of the relevant student objective, without pausing to go through the solution of each problem individually.
Sprints Sprints are designed to develop fluency. They should be fun, adrenaline-rich activities that intentionally build energy and excitement. A fast pace is essential. During Sprint administration, teachers assume the role of athletic coaches. A rousing routine fuels studentsβ motivation to do their personal best. Student recognition of increasing success is critical, and so every improvement is acknowledged. (See the Sprint Delivery Script for the suggested means of acknowledging and celebrating student success.)
One Sprint has two parts with closely related problems on each. Students complete the two parts of the Sprint in quick succession with the goal of improving on the second part, even if only by one more. The problems on the second Sprint should not be harder, or easier, than the problems on the first Sprint. The problems on a Sprint should progress from easiest to hardest. The first quarter of problems on the Sprint should be simple enough that all students find them accessible (though not all students will finish the first quarter of problems within one minute). The last quarter of problems should be challenging enough that even the strongest students in the class find them challenging.
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Sprints scores are not recorded. Thus, there is no need for students to write their names on the Sprints. The low-stakes nature of the exercise means that even students with allowances for extended time can participate. When a particular student finds the experience undesirable, it is reasonable to either give the student a copy of the sprint to practice with the night before, or to allow the student to opt out and take the Sprint home.
With practice, the Sprint routine takes about 8 minutes.
Sprint Delivery Script
Gather the following: stopwatch, a copy of Sprint A for each student, a copy of Sprint B for each student, answers for Sprint A and Sprint B. The following delineates a script for delivery of a pair of Sprints.
This sprint covers: topic.
Do not look at the Sprint; keep it turned face down on your desk.
There are xx problems on the Sprint. You will have 60 seconds. Do as many as you can. I do not expect any of you to finish.
On your mark, get set, GO.
60 seconds of silence.
STOP. Circle the last problem you completed.
I will read the answers. You say βYESβ if your answer matches. Mark the ones you have wrong by circling the number of the problem. Donβt try to correct them.
Energetically, rapid-fire call the answers ONLY.
Stop reading answers after there are no more students answering, βYes.β
Fantastic! Count the number you have correct, and write it on the top of the page. This is your personal goal for Sprint B.
Raise your hand if you have 1 or more correct. 2 or more, 3 or more...
Let us all applaud our runner-up, [insert name], with x correct. And let us applaud our winner, [insert name], with x correct.
You have a few minutes to finish up the page and get ready for the next Sprint.
Students are allowed to talk and ask for help; let this part last as long as most are working seriously.
Stop working. I will read the answers again so you can check your work. You say βYESβ if your answer matches.
Energetically, rapid-fire call the answers ONLY.
Optionally, ask students to stand, and lead them in an energy-expanding exercise that also keeps the brain going. Examples are jumping jacks or arm circles, etc., while counting by 15βs starting at 15, going up to 150 and back down to 0. You can follow this first exercise with a cool down exercise of a similar nature, such as
calf raises with counting by one-sixths (1
6,
1
3,
1
2,
2
3,
5
6, 1 β¦ ).
Hand out the second Sprint, and continue reading the script.
Keep the Sprint face down on your desk.
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There are xx problems on the Sprint. You will have 60 seconds. Do as many as you can. Your goal is to improve your score from the first Sprint.
On your mark, get set, GO.
60 seconds of silence.
STOP. Circle the last problem you completed.
I will read the answers. You say βYESβ if your answer matches. Mark the ones you have wrong by circling the number of the problem. Donβt try to correct them.
Quickly read the answers ONLY.
Count the number you have correct, and write it on the top of the page. Write the amount by which your score improved at the top of the page and circle it.
Raise your hand if you have 1 or more correct. 2 or more, 3 or more, ...
Let us all applaud our runner-up, [insert name], with x correct. And let us applaud our winner, [insert name], with x correct.
Raise your hand if you improved your score by 1 or more. 2 or more, 3 or more, ...
Let us all applaud our runner-up for most improved, [insert name]. And let us applaud our winner for most improved, [insert name].
You can take the Sprint home and finish it if you want.
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Grade 6 Mapping of Fluency Exercises to Fluency Requirements The following table lists all fluency exercises provided for use in Grade 6; footnotes by the related standard
indicate whether fluency is specifically called for by the standard itself and/or by the PARCC Model Content
Frameworks for Mathematics. Depending on the level of skill of the students, it may be appropriate to
supplement these exercises with additional fluency exercises from Grades 3β5 of A Story of Units.
The table also indicates the earliest recommended useβin all cases, fluency exercises should not be
conducted until after conceptual understanding has been taught and achieved through the lessons in A Story
of Ratios. Below the table, the text of each related standard is provided for reference.
Grade 6 Fluency Exercises
Related Standard
Fluency Exercise Earliest Recommended Use
5.NF.B.4 SprintβMultiplication of Fractions I Grade 6, Module 1
5.NF.B.4 SprintβMultiplication of Fractions II Grade 6, Module 1
6.NS.A.1 SprintβDivision of Fractions I Grade 6, Module 2
6.NS.A.1 SprintβDivision of Fractions II Grade 6, Module 2
6.NS.B.2 RWBEβLong Division Algorithm Grade 6, Module 2
6.NS.B.3* RWBEβAddition of Decimals Grade 6, Module 2
6.NS.B.3* SprintβAddition of Decimals I Grade 6, Module 2
6.NS.B.3* SprintβAddition of Decimals II Grade 6, Module 2
6.NS.B.3* RWBEβSubtraction of Decimals Grade 6, Module 2
6.NS.B.3* SprintβSubtraction of Decimals Grade 6, Module 2
6.NS.B.3* RWBEβMultiplication of Decimals Grade 6, Module 2
Identified by the PARCC Model Content Frameworks for Mathematics in the section Key Fluencies and Examples of Culminating Standards Standard explicitly calls for fluency by using the word fluent or fluently. No footnote: This activity supports procedural fluency as an instructional shift. It is necessary to pursue this shift in conjunction with conceptual understanding/application in the context of this standard.
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6.NS.B.3* SprintβMultiplication of Decimals I Grade 6, Module 2
6.NS.B.3* SprintβMultiplication of Decimals II Grade 6, Module 2
6.NS.B.4 SprintβGreatest Common Factor Grade 6, Module 2
6.NS.C.7a SprintβRational Numbers: Inequality Statements Grade 6, Module 3
6.EE.B.7 SprintβAddition and Subtraction Equations Grade 6, Module 4
6.EE.B.7 RWBEβMultiplication and Division Equations with Fractions Grade 6, Module 4
6.G.A.1 RWBEβArea of Shapes Grade 6, Module 5
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
5.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
a. Interpret the product (a/b) Γ q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a Γ q Γ· b. For example, use a visual fraction model to show (2/3) Γ 4 = 8/3, and create a story context for this equation. Do the same with (2/3) Γ (4/5) = 8/15. (In general, (a/b) Γ (c/d) = ac/bd.)
b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
6.NS.A.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) Γ· (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) Γ· (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) Γ· (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?
Compute fluently with multi-digit numbers and find common factors and multiples.
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6.NS.B.2 Fluently divide multi-digit numbers using the standard algorithm.
6.NS.B.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
6.NS.B.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1β100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4(9 + 2).
Apply and extend previous understandings of numbers to the system of rational numbers.
6.NS.C.7a Understand ordering and absolute value of rational numbers.
a. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret β3 > β7 as a statement that β3 is located to the right of β7 on a number line oriented from left to right.
Reason about and solve one-variable equations and inequalities.
6.EE.B.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
Solve real-world and mathematical problems involving area, surface area, and volume.
6.G.A.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by
composing into rectangles or decomposing into triangles and other shapes; apply these
techniques in the context of solving real-world and mathematical problems.
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Grade 7 Mapping of Fluency Exercises to Fluency Requirements The following table lists all fluency exercises provided for use in Grade 7; footnotes by the related standard
indicate whether fluency is specifically called for by the PARCC Model Content Frameworks for Mathematics.
(Note that there are no standards in Grade 7 that call for fluency explicitly by use of the word fluent or
fluently.) Depending on the level of skill of the students, it may be appropriate to supplement these exercises
with additional fluency exercises from Grade 6 and/or from Grades 3β5 of A Story of Units.
The table also indicates the earliest recommended useβin all cases, fluency exercises should not be
conducted until after conceptual understanding has been taught and achieved through the lessons in A Story
of Ratios. Below the table, the text of each related standard is provided for reference.
Grade 7 Fluency Exercises
Related Standard
Fluency Exercise Earliest Recommended Use
7.NS.A.2c SprintβInteger Addition Grade 7, Module 2
7.NS.A.2c SprintβInteger Subtraction Grade 7, Module 2
7.NS.A.2c SprintβInteger Multiplication Grade 7, Module 2
7.NS.A.2c SprintβInteger Division Grade 7, Module 2
7.EE.A.2 SprintβGenerating Equivalent Expressions Grade 7, Module 3
7.EE.B.3 RWBEβEquations Grade 7, Module 3
7.EE.B.4b RWBEβInequalities Grade 7, Module3
7.RP.A.3 SprintβFractions, Decimals, Percents Grade 7, Module 4
7.RP.A.3 SprintβPart, Whole, Percent Grade 7, Module 4
7.RP.A.3 SprintβPercent More or Less Grade 7, Module 4
7.RP.A.3 SprintβFractional Percents Grade 7, Module 4
Identified by the PARCC Model Content Frameworks for Mathematics in the section Key Fluencies and Examples of Culminating Standards
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Analyze proportional relationships and use them to solve real-world and mathematical problems.
7.RP.A.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
7.NS.A.2c Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
c. Apply properties of operations as strategies to multiply and divide rational numbers.
Use properties of operations to generate equivalent expressions.
7.EE.A.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that βincrease by 5%β is the same as βmultiply by 1.05.β
Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
7.EE.B.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
7.EE.B.4b Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.
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Grade 8 Mapping of Fluency Requirements to Fluency Exercises The following table lists all fluency exercises provided for use in Grade 8; footnotes by the related standard
indicate whether fluency is specifically called for by the PARCC Model Content Frameworks for Mathematics.
(Note that there are no standards in Grade 8 that call for fluency explicitly by use of the word fluent or
fluently.) Depending on the level of skill of the students, it may be appropriate to supplement these exercises
with additional fluency exercises from Grades 6 and 7.
The table also indicates the earliest recommended useβin all cases, fluency exercises should not be
conducted until after conceptual understanding has been taught and achieved through the lessons in A Story
of Ratios. Below the table, the text of each related standard is provided for reference.
Grade 8 Fluency Exercises
Related Standard
Fluency Exercise Earliest Recommended Use
8.EE.A.1 SprintβEquivalent Expressions in Exponential Notation I Grade 8, Module 1
8.EE.A.1 SprintβEquivalent Expressions in Exponential Notation II Grade 8, Module 1
8.EE.A.4 RWBEβOperations with Numbers Expressed in Scientific Notation I
Grade 8, Module 1
8.EE.A.4 RWBE β Operations with Numbers Expressed in Scientific Notation II
Grade 8, Module 1
8.EE.C.7 RWBEβMultistep Equations I Grade 8, Module 5
8.EE.C.7 RWBEβMultistep Equations II Grade 8, Module 5
8.EE.C.7 RWBE β Multistep Equations III Grade 8, Module 5
8.G.C.9 RWBEβArea and Volume I Grade 8, Module 7
8.G.C.9 RWBEβArea and Volume II Grade 8, Module 7
Identified by the PARCC Model Content Frameworks for Mathematics in the section Key Fluencies and Examples of Culminating Standards
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Work with radicals and integer exponents.
8.EE.A.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 Γ 3β5 = 3β3 = 1/33 = 1/27.
8.EE.A.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.
Analyze and solve linear equations and pairs of simultaneous linear equations.
8.EE.C.7 Solve linear equations in one variable.
a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
8.G.C.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
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Multiplication of Fractions IβRound 1
Directions: Determine the product of the fractions.
1. 1
2Γ
3
4 16.
8
9Γ
3
4
2. 5
6Γ
5
7 17.
3
4Γ
4
7
3. 3
4Γ
7
8 18.
1
4Γ
8
9
4. 4
5Γ
8
9 19.
3
5Γ
10
11
5. 1
4Γ
3
7 20.
8
13Γ
7
24
6. 5
7Γ
4
9 21. 2
1
2Γ 3
3
4
7. 3
5Γ
1
8 22. 1
4
5Γ 6
1
3
8. 2
9Γ
7
9 23. 8
2
7Γ 4
5
6
9. 1
3Γ
2
5 24. 5
2
5Γ 2
1
8
10. 3
7Γ
5
8 25. 4
6
7Γ 1
1
4
11. 2
3Γ
9
10 26. 2
2
3Γ 4
2
5
12. 3
5Γ
1
6 27. 6
9
10Γ 7
1
3
13. 2
7Γ
3
4 28. 1
3
8Γ 4
2
5
14. 5
8Γ
3
10 29. 3
5
6Γ 2
4
15
15. 4
5Γ
7
8 30. 4
1
3Γ 5
Number Correct: ______
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Multiplication of Fractions IβRound 1 [KEY]
Directions: Determine the product of the fractions.
1. 1
2Γ
3
4
π
π 16.
8
9Γ
3
4
ππ
ππ=
π
π
2. 5
6Γ
5
7
ππ
ππ 17.
3
4Γ
4
7
ππ
ππ=
π
π
3. 3
4Γ
7
8
ππ
ππ 18.
1
4Γ
8
9
π
ππ=
π
π
4. 4
5Γ
8
9
ππ
ππ 19.
3
5Γ
10
11
ππ
ππ=
π
ππ
5. 1
4Γ
3
7
π
ππ 20.
8
13Γ
7
24
ππ
πππ=
π
ππ
6. 5
7Γ
4
9
ππ
ππ 21. 2
1
2Γ 3
3
4
ππ
π= π
π
π
7. 3
5Γ
1
8
π
ππ 22. 1
4
5Γ 6
1
3
πππ
ππ= ππ
π
π
8. 2
9Γ
7
9
ππ
ππ 23. 8
2
7Γ 4
5
6
ππππ
ππ= ππ
π
ππ
9. 1
3Γ
2
5
π
ππ 24. 5
2
5Γ 2
1
8
πππ
ππ= ππ
ππ
ππ
10. 3
7Γ
5
8
ππ
ππ 25. 4
6
7Γ 1
1
4
πππ
ππ= π
π
ππ
11. 2
3Γ
9
10
ππ
ππ=
π
π 26. 2
2
3Γ 4
2
5
πππ
ππ= ππ
ππ
ππ
12. 3
5Γ
1
6
π
ππ=
π
ππ 27. 6
9
10Γ 7
1
3
ππππ
ππ= ππ
π
π
13. 2
7Γ
3
4
π
ππ=
π
ππ 28. 1
3
8Γ 4
2
5
πππ
ππ= π
π
ππ
14. 5
8Γ
3
10
ππ
ππ=
π
ππ 29. 3
5
6Γ 2
4
15
πππ
ππ= π
ππ
ππ
15. 4
5Γ
7
8
ππ
ππ=
π
ππ 30. 4
1
3Γ 5
ππ
π= ππ
π
π
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Multiplication of Fractions IβRound 2
Directions: Determine the product of the fractions.
1. 5
6Γ
1
4 16.
3
7Γ
2
9
2. 2
3Γ
5
7 17.
4
5Γ
10
13
3. 1
3Γ
2
5 18.
2
9Γ
3
8
4. 5
7Γ
5
8 19.
1
8Γ
4
5
5. 3
8Γ
7
9 20.
3
7Γ
2
15
6. 3
4Γ
5
6 21. 1
1
2Γ 4
3
4
7. 2
7Γ
3
8 22. 2
5
6Γ 3
3
8
8. 1
4Γ
3
4 23. 1
7
8Γ 5
1
5
9. 5
8Γ
3
10 24. 6
2
3Γ 2
3
8
10. 6
11Γ
1
2 25. 7
1
2Γ 3
6
7
11. 6
7Γ
5
8 26. 3 Γ 4
1
3
12. 1
6Γ
9
10 27. 2
3
5Γ 5
1
6
13. 3
4Γ
8
9 28. 4
2
5Γ 7
14. 5
6Γ
2
3 29. 1
4
7Γ 2
1
2
15. 1
4Γ
8
11 30. 3
5
6Γ
3
10
Number Correct: ______
Improvement: ______
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Multiplication of Fractions IβRound 2 [KEY]
Directions: Determine the product of the fractions.
1. 5
6Γ
1
4
π
ππ 16.
3
7Γ
2
9
π
ππ=
π
ππ
2. 2
3Γ
5
7
ππ
ππ 17.
4
5Γ
10
13
ππ
ππ=
π
ππ
3. 1
3Γ
2
5
π
ππ 18.
2
9Γ
3
8
π
ππ=
π
ππ
4. 5
7Γ
5
8
ππ
ππ 19.
1
8Γ
4
5
π
ππ=
π
ππ
5. 3
8Γ
7
9
ππ
ππ=
π
ππ 20.
3
7Γ
2
15
π
πππ=
π
ππ
6. 3
4Γ
5
6
ππ
ππ=
π
π 21. 1
1
2Γ 4
3
4
ππ
π= π
π
π
7. 2
7Γ
3
8
π
ππ=
π
ππ 22. 2
5
6Γ 3
3
8
πππ
ππ= π
π
ππ
8. 1
4Γ
3
4
π
ππ 23. 1
7
8Γ 5
1
5
πππ
ππ= π
π
π
9. 5
8Γ
3
10
ππ
ππ=
π
ππ 24. 6
2
3Γ 2
3
8
πππ
ππ= ππ
π
π
10. 6
11Γ
1
2
π
ππ=
π
ππ 25. 7
1
2Γ 3
6
7
πππ
ππ= ππ
ππ
ππ
11. 6
7Γ
5
8
ππ
ππ=
ππ
ππ 26. 3 Γ 4
1
3
ππ
π= ππ
12. 1
6Γ
9
10
π
ππ=
π
ππ 27. 2
3
5Γ 5
1
6
πππ
ππ= ππ
ππ
ππ
13. 3
4Γ
8
9
ππ
ππ=
π
π 28. 4
2
5Γ 7
πππ
π= ππ
π
π
14. 5
6Γ
2
3
ππ
ππ=
π
π 29. 1
4
7Γ 2
1
2
ππ
ππ= π
ππ
ππ
15. 1
4Γ
8
11
π
ππ=
π
ππ 30. 3
5
6Γ
3
10
ππ
ππ= π
π
ππ
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Multiplication of Fractions IIβRound 1
Directions: Determine the product of the fractions.
1. 1
2Γ
5
8 16.
2
9Γ
3
8
2. 3
4Γ
3
5 17.
3
8Γ
8
9
3. 1
4Γ
7
8 18.
3
4Γ
7
9
4. 3
9Γ
2
5 19.
3
5Γ
10
13
5. 5
8Γ
3
7 20. 1
2
7Γ
7
8
6. 3
7Γ
4
9 21. 3
1
2Γ 3
5
6
7. 2
5Γ
3
8 22. 1
7
8Γ 5
1
5
8. 4
9Γ
5
9 23. 5
4
5Γ 3
2
9
9. 2
3Γ
5
7 24. 7
2
5Γ 2
3
8
10. 2
7Γ
3
10 25. 4
2
3Γ 2
3
10
11. 3
4Γ
9
10 26. 3
3
5Γ 6
1
4
12. 3
5Γ
2
9 27. 2
7
9Γ 5
1
3
13. 2
10Γ
5
6 28. 4
3
8Γ 3
1
5
14. 5
8Γ
7
10 29. 3
1
3Γ 5
2
5
15. 3
5Γ
7
9 30. 2
2
3Γ 7
Number Correct: ______
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Multiplication of Fractions IIβRound 1 [KEY]
Directions: Determine the product of the fractions.
1. 1
2Γ
5
8
π
ππ 16.
2
9Γ
3
8
π
ππ=
π
ππ
2. 3
4Γ
3
5
π
ππ 17.
3
8Γ
8
9
ππ
ππ=
π
π
3. 1
4Γ
7
8
π
ππ 18.
3
4Γ
7
9
ππ
ππ=
π
ππ
4. 3
9Γ
2
5
π
ππ 19.
3
5Γ
10
13
ππ
ππ=
π
ππ
5. 5
8Γ
3
7
ππ
ππ 20. 1
2
7Γ
7
8
ππ
ππ= π
π
π
6. 3
7Γ
4
9
ππ
ππ 21. 3
1
2Γ 3
5
6
πππ
ππ= ππ
π
ππ
7. 2
5Γ
3
8
π
ππ=
π
ππ 22. 1
7
8Γ 5
1
5
πππ
ππ= π
π
π
8. 4
9Γ
5
9
ππ
ππ 23. 5
4
5Γ 3
2
9
πππ
ππ= ππ
ππ
ππ
9. 2
3Γ
5
7
ππ
ππ 24. 7
2
5Γ 2
3
8
πππ
ππ= ππ
ππ
ππ
10. 2
7Γ
3
10
π
ππ=
π
ππ 25. 4
2
3Γ 2
3
10
πππ
ππ= ππ
ππ
ππ
11. 3
4Γ
9
10
ππ
ππ 26. 3
3
5Γ 6
1
4
πππ
ππ= ππ
π
π
12. 3
5Γ
2
9
π
ππ=
π
ππ 27. 2
7
9Γ 5
1
3
πππ
ππ= ππ
ππ
ππ
13. 2
10Γ
5
6
ππ
ππ=
π
π 28. 4
3
8Γ 3
1
5
πππ
ππ= ππ
14. 5
8Γ
7
10
ππ
ππ=
π
ππ 29. 3
1
3Γ 5
2
5
πππ
ππ= ππ
15. 3
5Γ
7
9
ππ
ππ=
π
ππ 30. 2
2
3Γ 7
ππ
π= ππ
π
π
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Multiplication of Fractions IIβRound 2
Directions: Determine the product of the fractions.
1. 2
3Γ
5
7 16.
3
11Γ
2
9
2. 1
4Γ
3
5 17.
3
5Γ
10
21
3. 2
3Γ
2
5 18.
4
9Γ
3
10
4. 5
9Γ
5
8 19.
3
8Γ
4
5
5. 5
8Γ
3
7 20.
6
11Γ
2
15
6. 3
4Γ
7
8 21. 1
2
3Γ
3
5
7. 2
5Γ
3
8 22. 2
1
6Γ
3
4
8. 3
4Γ
3
4 23. 1
2
5Γ 3
2
3
9. 7
8Γ
3
10 24. 4
2
3Γ 1
1
4
10. 4
9Γ
1
2 25. 3
1
2Γ 2
4
5
11. 6
11Γ
3
8 26. 3 Γ 5
3
4
12. 5
6Γ
9
10 27. 1
2
3Γ 3
1
4
13. 3
4Γ
2
9 28. 2
3
5Γ 3
14. 4
11Γ
5
8 29. 1
5
7Γ 3
1
2
15. 2
3Γ
9
10 30. 3
1
3Γ 1
9
10
Number Correct: ______
Improvement: ______
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Multiplication of Fractions IIβRound 2 [KEY]
Directions: Determine the product of the fractions.
1. 2
3Γ
5
7
ππ
ππ 16.
3
11Γ
2
9
π
ππ=
π
ππ
2. 1
4Γ
3
5
π
ππ 17.
3
5Γ
10
21
ππ
πππ=
π
π
3. 2
3Γ
2
5
π
ππ 18.
4
9Γ
3
10
ππ
ππ=
π
ππ
4. 5
9Γ
5
8
ππ
ππ 19.
3
8Γ
4
5
ππ
ππ=
π
ππ
5. 5
8Γ
3
7
ππ
ππ 20.
6
11Γ
2
15
ππ
πππ=
π
ππ
6. 3
4Γ
7
8
ππ
ππ 21. 1
2
3Γ
3
5
ππ
ππ= π
7. 2
5Γ
3
8
π
ππ=
π
ππ 22. 2
1
6Γ
3
4
ππ
ππ= π
ππ
ππ= π
π
π
8. 3
4Γ
3
4
π
ππ 23. 1
2
5Γ 3
2
3
ππ
ππ= π
π
ππ
9. 7
8Γ
3
10
ππ
ππ 24. 4
2
3Γ 1
1
4
ππ
ππ= π
ππ
ππ = π
π
π
10. 4
9Γ
1
2
π
ππ=
π
π 25. 3
1
2Γ 2
4
5
ππ
ππ= π
π
ππ= π
π
π
11. 6
11Γ
3
8
ππ
ππ=
π
ππ 26. 3 Γ 5
3
4
ππ
π= ππ
π
π
12. 5
6Γ
9
10
ππ
ππ=
π
π 27. 1
2
3Γ 3
1
4
ππ
ππ= π
π
ππ
13. 3
4Γ
2
9
π
ππ=
π
π 28. 2
3
5Γ 3
ππ
π= π
π
π
14. 4
11Γ
5
8
ππ
ππ=
π
ππ 29. 1
5
7Γ 3
1
2
ππ
ππ= π
15. 2
3Γ
9
10
ππ
ππ=
π
π 30. 3
1
3Γ 1
9
10
πππ
ππ= π
ππ
ππ= π
π
π
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Division of Fractions β Round 1
Directions: Evaluate each expression. Place the final answer in the last column in each section.
1. 9 ones Γ· 3 ones 23. 6
10 Γ·
4
10
2. 9 Γ· 3 24. 6
10Γ·
2
5=
6
10Γ·
10
3. 9 tens Γ· 3 tens 25. 10
12Γ·
5
12
4. 90 Γ· 30 26. 5
6Γ·
5
12=
12Γ·
5
12
5. 9 hundreds Γ· 3 hundreds 27. 10
12Γ·
3
12
6. 900 Γ· 300 28. 10
12Γ·
1
4=
10
12Γ·
12
7. 9 halves Γ· 3 halves 29. 5
6Γ·
3
12=
12Γ·
3
12
8. 9
2 Γ·
3
2 30.
5
10Γ·
2
10
9. 9 fourths Γ· 3 fourths 31. 5
10Γ·
1
5=
5
10Γ·
10
10. 9
4 Γ·
3
4 32.
1
2Γ·
2
10=
10Γ·
2
10
11. 9
8 Γ·
3
8 33.
1
2Γ·
1
5=
10Γ·
10
12. 2
3 Γ·
1
3 34.
1
2Γ·
2
4
13. 1
3 Γ·
2
3 35.
3
4Γ·
2
8
14. 6
7 Γ·
2
7 36.
1
2Γ·
3
8
15. 5
7 Γ·
2
7 37.
2
3Γ·
1
6
16. 3
7 Γ·
4
7 38.
1
3Γ·
4
9
17. 6
10 Γ·
2
10 39.
5
9Γ·
2
3
18. 6
10 Γ·
4
10 40.
5
6Γ·
2
12
19. 6
10 Γ·
8
10 41.
2
3Γ·
5
12
20. 7
12 Γ·
2
12 42.
5
12Γ·
1
2
21. 6
12 Γ·
9
12 43.
2
7Γ·
3
14
22. 4
12 Γ·
11
12
44. 2
7Γ·
9
14
Number Correct: ______
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Division of Fractions β Round 1 [KEY]
Directions: Evaluate each expression. Place the final answer in the last column in each section.
1. 9 ones Γ· 3 ones π
π= π 23.
6
10 Γ·
4
10
π
π= π
π
π
2. 9 Γ· 3 π
π= π 24.
6
10Γ·
2
5=
6
10Γ·
10
π
π= π
π
π
3. 9 tens Γ· 3 tens π
π= π 25.
10
12Γ·
5
12
ππ
π= π
4. 90 Γ· 30 π
π= π 26.
5
6Γ·
5
12=
12Γ·
5
12
ππ
π= π
5. 9 hundreds Γ· 3 hundreds π
π= π 27.
10
12Γ·
3
12
ππ
π= π
π
π
6. 900 Γ· 300 π
π= π 28.
10
12Γ·
1
4=
10
12Γ·
12
ππ
π= π
π
π
7. 9 halves Γ· 3 halves π
π= π 29.
5
6Γ·
3
12=
12Γ·
3
12
ππ
π= π
π
π
8. 9
2 Γ·
3
2
π
π= π 30.
5
10Γ·
2
10
π
π= π
π
π
9. 9 fourths Γ· 3 fourths π
π= π 31.
5
10Γ·
1
5=
5
10Γ·
10
π
π= π
π
π
10. 9
4 Γ·
3
4
π
π= π 32.
1
2Γ·
2
10=
10Γ·
2
10
π
π= π
π
π
11. 9
8 Γ·
3
8
π
π= π 33.
1
2Γ·
2
4
π
π= π
12. 2
3 Γ·
1
3
π
π= π 34.
3
4Γ·
2
8 π
13. 1
3 Γ·
2
3
π
π 35.
1
2Γ·
3
8
π
π= π
π
π
14. 6
7 Γ·
2
7
π
π= π 36.
1
2Γ·
1
5=
10Γ·
10
π
π= π
π
π
15. 5
7 Γ·
2
7
π
π= π
π
π 37.
2
4Γ·
1
3
π
π= π
π
π
16. 3
7 Γ·
4
7
π
π 38.
1
4Γ·
4
6
π
π
17. 6
10 Γ·
2
10
π
π= π 39.
3
4Γ·
2
6
π
π= π
π
π
18. 6
10 Γ·
4
10
π
π= π
π
π 40.
5
6Γ·
1
4
ππ
π= π
π
π
19. 6
10 Γ·
8
10
π
π=
π
π 41.
2
9Γ·
5
6
π
ππ
20. 7
12 Γ·
2
12
π
π= π
π
π 42.
5
9Γ·
1
6
ππ
π= π
21. 6
12 Γ·
9
12
π
π=
π
π 43.
1
2Γ·
1
7
π
π= π
π
π
22. 4
12 Γ·
11
12
π
ππ 44.
5
7Γ·
1
2
ππ
π= π
π
π
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Number Correct: ______
Improvement: ______
Sprint Title β Round 2
Directions: Evaluate each expression. Place the final answer in the last column in each section
1. 12 ones Γ· 2 ones 23. 6
12 Γ·
4
12
2. 12 Γ· 2 24. 6
12Γ·
2
6=
6
12Γ·
12
3. 12 tens Γ· 2 tens 25. 8
14Γ·
7
14
4. 120 Γ· 20 26. 8
14Γ·
1
2=
8
14Γ·
14
5. 12 hundreds Γ· 2 hundreds 27. 11
14Γ·
2
14
6. 1,200 Γ· 200 28. 11
14Γ·
1
7=
11
14Γ·
14
7. 12 halves Γ· 2 halves 29. 1
7Γ·
6
14=
14Γ·
6
14
8. 12
2 Γ·
2
2 30.
7
18Γ·
3
18
9. 12 fourths Γ· 3 fourths 31. 7
18Γ·
1
6=
7
18Γ·
18
10. 12
4 Γ·
3
4 32.
1
3Γ·
12
18=
18Γ·
12
18
11. 12
8 Γ·
3
8 33.
1
6Γ·
4
18
12. 2
4 Γ·
1
4 34.
4
12Γ·
8
6
13. 1
4 Γ·
2
4 35.
1
3Γ·
3
15
14. 4
5 Γ·
2
5 36.
2
6Γ·
1
9=
18Γ·
18
15. 2
5 Γ·
4
5 37.
1
6Γ·
4
9
16. 3
5 Γ·
4
5 38.
2
3Γ·
3
4
17. 6
8 Γ·
2
8 39.
1
3Γ·
3
5
18. 6
8 Γ·
4
8 40.
1
7Γ·
1
2
19. 6
8 Γ·
5
8 41.
5
6Γ·
2
9
20. 6
10 Γ·
2
10 42.
5
9Γ·
2
6
21. 7
10 Γ·
8
10 43.
5
6Γ·
4
9
22. 4
10 Γ·
7
10 44.
1
2Γ·
4
5
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Sprint Title β Round 2 [KEY]
Directions: Evaluate each expression. Place the final answer in the last column in each section
1. 12 ones Γ· 2 ones ππ
π= π 23.
6
12 Γ·
4
12
π
π= π
π
π
2. 12 Γ· 2 ππ
π= π 24.
6
12Γ·
2
6=
6
12Γ·
12
π
π= π
π
π
3. 12 tens Γ· 2 tens ππ
π= π 25.
8
14Γ·
7
14
π
π= π
π
π
4. 120 Γ· 20 ππ
π= π 26.
8
14Γ·
1
2=
8
14Γ·
14
π
π= π
π
π
5. 12 hundreds Γ· 2 hundreds ππ
π= π 27.
11
14Γ·
2
14
ππ
π= π
π
π
6. 1,200 Γ· 200 ππ
π= π 28.
11
14Γ·
1
7=
11
14Γ·
14
ππ
π= π
π
π
7. 12 halves Γ· 2 halves ππ
π= π 29.
1
7Γ·
6
14=
14Γ·
6
14
π
π=
π
π
8. 12
2 Γ·
2
2
ππ
π= π 30.
7
18Γ·
3
18
π
π= π
π
π
9. 12 fourths Γ· 3 fourths ππ
π= π 31.
7
18Γ·
1
6=
7
18Γ·
18
π
π= π
π
π
10. 12
4 Γ·
3
4
ππ
π= π 32.
1
3Γ·
12
18=
18Γ·
12
18
π
ππ=
π
π
11. 12
8 Γ·
3
8
ππ
π= π 33.
1
6Γ·
4
18
π
π
12. 2
4 Γ·
1
4
π
π= π 34.
4
12Γ·
8
6
π
ππ=
π
π
13. 1
4 Γ·
2
4
π
π 35.
1
3Γ·
3
15
π
π= π
π
π
14. 4
5 Γ·
2
5
π
π= π 36.
2
6Γ·
1
9=
18Γ·
18
π
π= π
15. 2
5 Γ·
4
5
π
π=
π
π 37.
1
6Γ·
4
9
π
π
16. 3
5 Γ·
4
5
π
π 38.
2
3Γ·
3
4
π
π
17. 6
8 Γ·
2
8
π
π= π 39.
1
3Γ·
3
5
π
π
18. 6
8 Γ·
4
8
π
π= π
π
π 40.
1
7Γ·
1
2
π
π
19. 6
8 Γ·
5
8
π
π= π
π
π 41.
5
6Γ·
2
9
ππ
π= π
π
π
20. 6
10 Γ·
2
10
π
π= π 42.
5
9Γ·
2
6
ππ
π= π
π
π
21. 7
10 Γ·
8
10
π
π 43.
5
6Γ·
4
9
ππ
π= π
π
π
22. 4
10 Γ·
7
10
π
π 44.
1
2Γ·
4
5
π
π
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Division of Fractions IIβRound 1
Directions: Determine the quotient of the fractions.
1. 4
10Γ·
2
10 16. 3
1
8Γ·
2
3
2. 9
12Γ·
3
12 17. 1
5
6Γ·
1
2
3. 6
10Γ·
4
10 18.
5
8Γ· 2
3
4
4. 2
8Γ·
3
8 19.
1
3Γ· 1
4
5
5. 2
7Γ·
6
7 20.
3
4Γ· 2
3
10
6. 11
9Γ·
8
9 21. 2
1
5Γ· 1
1
6
7. 5
13Γ·
10
13 22. 2
4
9Γ· 1
3
5
8. 7
8Γ·
13
16 23. 1
2
9Γ· 3
2
5
9. 3
5Γ·
7
10 24. 2
2
3Γ· 3
10. 9
30Γ·
3
5 25. 1
3
4Γ· 2
2
5
11. 1
3Γ·
4
5 26. 4 Γ· 1
2
9
12. 2
5Γ·
3
4 27. 3
1
5Γ· 6
13. 3
4Γ·
5
9 28. 2
5
6Γ· 1
1
3
14. 4
5Γ·
7
12 29. 10
2
3Γ· 8
15. 3
8Γ·
5
2 30. 15 Γ· 2
3
5
Number Correct: ______
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Division of Fractions IIβRound 1 [KEY]
Directions: Determine the quotient of the fractions.
1. 4
10Γ·
2
10
π
π= π 16. 3
1
8Γ·
2
3
ππ
ππ= π
ππ
ππ
2. 9
12Γ·
3
12
π
π= π 17. 1
5
6Γ·
1
2
ππ
π=
ππ
π= π
π
π
3. 6
10Γ·
4
10
π
π=
π
π= π
π
π 18.
5
8Γ· 2
3
4
ππ
ππ=
π
ππ
4. 2
8Γ·
3
8
π
π 19.
1
3Γ· 1
4
5
π
ππ
5. 2
7Γ·
6
7
π
π=
π
π 20.
3
4Γ· 2
3
10
ππ
ππ=
ππ
ππ
6. 11
9Γ·
8
9
ππ
π= π
π
π 21. 2
1
5Γ· 1
1
6
ππ
ππ= π
ππ
ππ
7. 5
13Γ·
10
13
π
ππ=
π
π 22. 2
4
9Γ· 1
3
5
πππ
ππ=
ππ
ππ= π
ππ
ππ
8. 7
8Γ·
13
16
ππ
ππ= π
π
ππ 23. 1
2
9Γ· 3
2
5
ππ
πππ
9. 3
5Γ·
7
10
π
π 24. 2
2
3Γ· 3
π
π
10. 9
30Γ·
3
5
π
ππ=
π
π 25. 1
3
4Γ· 2
2
5
ππ
ππ
11. 1
3Γ·
4
5
π
ππ 26. 4 Γ· 1
2
9
ππ
ππ= π
π
ππ
12. 2
5Γ·
3
4
π
ππ 27. 3
1
5Γ· 6
ππ
ππ=
π
ππ
13. 3
4Γ·
5
9
ππ
ππ= π
π
ππ 28. 2
5
6Γ· 1
1
3
ππ
ππ= π
π
ππ= π
π
π
14. 4
5Γ·
7
12
ππ
ππ= π
ππ
ππ 29. 10
2
3Γ· 8
ππ
ππ=
π
π= π
π
π
15. 3
8Γ·
5
2
π
ππ=
π
ππ 30. 15 Γ· 2
3
5
πππ
π= ππ
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Division of Fractions IIβRound 2
Directions: Determine the quotient of the fractions.
1. 10
2Γ·
5
2 16.
5
8Γ· 1
3
4
2. 6
5Γ·
3
5 17.
1
4Γ· 2
2
5
3. 10
7Γ·
2
7 18. 2
3
5Γ·
3
8
4. 3
8Γ·
5
8 19. 1
3
5Γ·
2
9
5. 1
4Γ·
3
12 20. 4 Γ· 2
3
8
6. 7
5Γ·
3
10 21. 1
1
2Γ· 5
7. 8
15Γ·
4
5 22. 3
1
3Γ· 1
3
4
8. 5
6Γ·
5
12 23. 2
2
5Γ· 1
1
4
9. 3
5Γ·
7
9 24. 3
1
2Γ· 2
2
3
10. 3
10Γ·
3
9 25. 1
4
5Γ· 2
3
4
11. 3
4Γ·
7
9 26. 3
1
6Γ· 1
3
5
12. 7
10Γ·
3
8 27. 3
3
5Γ· 2
1
8
13. 4 Γ·4
9 28. 5 Γ· 1
1
6
14. 5
8Γ· 7 29. 3
3
4Γ· 5
1
2
15. 9 Γ·2
3 30. 4
2
3 Γ· 5
1
4
Number Correct: ______
Improvement: ______
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Division of Fractions IIβRound 2 [KEY]
Directions: Determine the quotient of the fractions.
1. 10
2Γ·
5
2
ππ
π= π 16.
5
8Γ· 1
3
4
ππ
ππ=
π
ππ
2. 6
5Γ·
3
5
π
π= π 17.
1
4Γ· 2
2
5
π
ππ
3. 10
7Γ·
2
7
ππ
π= π 18. 2
3
5Γ·
3
8
πππ
ππ= π
ππ
ππ
4. 3
8Γ·
5
8
π
π 19. 1
3
5Γ·
2
9
ππ
ππ= π
π
ππ= π
π
π
5. 1
4Γ·
3
12
π
π= π 20. 4 Γ· 2
3
8
ππ
ππ= π
π
ππ
6. 7
5Γ·
3
10
ππ
π= π
π
π 21. 1
1
2Γ· 5
π
ππ
7. 8
15Γ·
4
5
π
ππ=
π
π 22. 3
1
3Γ· 1
3
4
ππ
ππ= π
ππ
ππ
8. 5
6Γ·
5
12
ππ
π= π 23. 2
2
5Γ· 1
1
4
ππ
ππ= π
ππ
ππ
9. 3
5Γ·
7
9
ππ
ππ 24. 3
1
2Γ· 2
2
3
ππ
ππ= π
π
ππ
10. 3
10Γ·
3
9
ππ
ππ=
π
ππ 25. 1
4
5Γ· 2
3
4
ππ
ππ
11. 3
4Γ·
7
9
ππ
ππ 26. 3
1
6Γ· 1
3
5
ππ
ππ= π
ππ
ππ
12. 7
10Γ·
3
8
ππ
ππ=
ππ
ππ= π
ππ
ππ 27. 3
3
5Γ· 2
1
8
πππ
ππ= π
ππ
ππ
13. 4 Γ·4
9
ππ
π= π
π
π 28. 5 Γ· 1
1
6
ππ
π= π
π
π
14. 5
8Γ· 7
π
ππ 29. 3
3
4Γ· 5
1
2
ππ
ππ=
ππ
ππ
15. 9 Γ·2
3
ππ
π= π 30. 4
2
3 Γ· 5
1
4
ππ
ππ=
π
π
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Long Division Algorithm
Progression of Exercises
1. 3,282 Γ· 6
πππ
2. 2,712 Γ· 3
πππ
3. 15,036 Γ· 7
π, πππ
4. 1,788 Γ· 8
πππ. π
5. 5,736 Γ· 12
πππ
6. 35,472 Γ· 16
π, πππ
7. 13,384 Γ· 28
πππ
8. 31,317 Γ· 39
πππ
9. 1,113 Γ· 42
ππ. π
10. 4,082 Γ· 52
ππ. π
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Addition of Decimals I
Progression of Exercises
1. 1.3 + 2.1
π. π
2. 14.3 + 12.6
ππ. π
3. 56.56 + 12.12
ππ. ππ
4. 24.5 + 42.9
ππ. π
5. 365.8 + 127.4
πππ. π
6. 76.67 + 40.33
πππ
7. 872.78 + 135.86
π, πππ. ππ
8. 549.2 + 678.09
π, πππ. ππ
9. 821.3 + 106.87
πππ. ππ
10. 108.97 + 268.03
πππ
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Addition of Decimals II
Progression of Exercises
1. 4.2 + 3.5
π. π
2. 452. +53.7
ππ. π
3. 32.45 + 24.77
ππ. ππ
4. 16.87 + 17.3
ππ. ππ
5. 78.04 + 8.29
ππ. ππ
6. 247.12 + 356.78
πππ. π
7. 74.54 + 0.97
ππ. ππ
8. 154 + 85.3
πππ. π
9. 438.21 + 195.7
πππ. ππ
10. 0.648 + 3.08
π. πππ
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Addition of Decimals β Round 1
Directions: Evaluate each expression.
1. 5.1 + 6 23. 3.6 + 2.1
2. 5.1 + 0.6 24. 3.6 + 0.21
3. 5.1 + 0.06 25. 3.6 + 0.021
4. 5.1 + 0.006 26. 0.36 + 0.021
5. 5.1 + 0.0006 27. 0.036 + 0.021
6. 3 + 2.4 28. 1.4 + 42
7. 0.3 + 2.4 29. 1.4 + 4.2
8. 0.03 + 2.4 30. 1.4 + 0.42
9. 0.003 + 2.4 31. 1.4 + 0.042
10. 0.0003 + 2.4 32. 0.14 + 0.042
11. 24 + 0.3 33. 0.014 + 0.042
12. 2 + 0.3 34. 0.8 + 2
13. 0.2 + 0.03 35. 0.8 + 0.2
14. 0.02 + 0.3 36. 0.08 + 0.02
15. 0.2 + 3 37. 0.008 + 0.002
16. 2 + 0.03 38. 6 + 0.4
17. 5 + 0.4 39. 0.6 + 0.4
18. 0.5 + 0.04 40. 0.06 + 0.04
19. 0.05 + 0.4 41. 0.006 + 0.004
20. 0.5 + 4 42. 0.1 + 9
21. 5 + 0.04 43. 0.1 + 0.9
22. 0.5 + 0.4 44. 0.01 + 0.09
Number Correct: ______
6β8 Xβ’X
Fluency Support NYS COMMON CORE MATHEMATICS CURRICULUM
Fluency Support for Grades 6β8 Date: 4/2/15
35
Β© 2014 Common Core, Inc. Some rights reserved. commoncore.org This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Addition of Decimals β Round 1 [KEY]
Directions: Evaluate each expression.
1. 5.1 + 6 11.1 23. 3.6 + 2.1 5.7
2. 5.1 + 0.6 5.7 24. 3.6 + 0.21 3.81
3. 5.1 + 0.06 5.16 25. 3.6 + 0.021 3.621
4. 5.1 + 0.006 5.106 26. 0.36 + 0.021 0.381
5. 5.1 + 0.0006 5.1006 27. 0.036 + 0.021 0.057
6. 3 + 2.4 5.4 28. 1.4 + 42 43.4
7. 0.3 + 2.4 2.7 29. 1.4 + 4.2 5.6
8. 0.03 + 2.4 2.43 30. 1.4 + 0.42 1.82
9. 0.003 + 2.4 2.403 31. 1.4 + 0.042 1.442
10. 0.0003 + 2.4 2.4003 32. 0.14 + 0.042 0.182
11. 24 + 0.3 24.3 33. 0.014 + 0.042 0.056
12. 2 + 0.3 2.3 34. 0.8 + 2 2.8
13. 0.2 + 0.03 0.23 35. 0.8 + 0.2 1
14. 0.02 + 0.3 0.32 36. 0.08 + 0.02 0.1
15. 0.2 + 3 3.2 37. 0.008 + 0.002 0.01
16. 2 + 0.03 2.03 38. 6 + 0.4 6.4
17. 5 + 0.4 5.4 39. 0.6 + 0.4 1
18. 0.5 + 0.04 0.54 40. 0.06 + 0.04 0.1
19. 0.05 + 0.4 0.45 41. 0.006 + 0.004 0.01
20. 0.5 + 4 4.5 42. 0.1 + 9 9.1
21. 5 + 0.04 5.04 43. 0.1 + 0.9 1
22. 0.5 + 0.4 0.9 44. 0.01 + 0.09 0.1
6β8 Xβ’X
Fluency Support NYS COMMON CORE MATHEMATICS CURRICULUM
Fluency Support for Grades 6β8 Date: 4/2/15
36
Β© 2014 Common Core, Inc. Some rights reserved. commoncore.org This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Addition of Decimals β Round 2
Directions: Evaluate each expression.
1. 3.2 + 5 23. 4.2 + 5.5
2. 3.2 + 0.5 24. 4.2 + 0.55
3. 3.2 + 0.05 25. 4.2 + 0.055
4. 3.2 + 0.005 26. 0.42 + 0.055
5. 3.2 + 0.0005 27. 0.042 + 0.055
6. 4 + 5.3 28. 2.7 + 12
7. 0.4 + 5.3 29. 2.7 + 1.2
8. 0.04 + 5.3 30. 2.7 + 0.12
9. 0.004 + 5.3 31. 2.7 + 0.012
10. 0.0004 + 5.3 32. 0.27 + 0.012
11. 4 + 0.53 33. 0.027 + 0.012
12. 6 + 0.2 34. 0.7 + 3
13. 0.6 + 0.02 35. 0.7 + 0.3
14. 0.06 + 0.2 36. 0.07 + 0.03
15. 0.6 + 2 37. 0.007 + 0.003
16. 2 + 0.06 38. 5 + 0.5
17. 1 + 0.7 39. 0.5 + 0.5
18. 0.1 + 0.07 40. 0.05 + 0.05
19. 0.01 + 0.7 41. 0.005 + 0.005
20. 0.1 + 7 42. 0.2 + 8
21. 1 + 0.07 43. 0.2 + 0.8
22. 0.1 + 0.7 44. 0.02 + 0.08
Number Correct: ______
Improvement: ______
6β8 Xβ’X
Fluency Support NYS COMMON CORE MATHEMATICS CURRICULUM
Fluency Support for Grades 6β8 Date: 4/2/15
37
Β© 2014 Common Core, Inc. Some rights reserved. commoncore.org This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Addition of Decimals β Round 2 [KEY]
Directions: Evaluate each expression.
1. 3.2 + 5 8.2 23. 4.2 + 5.5 9.7
2. 3.2 + 0.5 3.7 24. 4.2 + 0.55 4.75
3. 3.2 + 0.05 3.25 25. 4.2 + 0.055 4.255
4. 3.2 + 0.005 3.205 26. 0.42 + 0.055 0.475
5. 3.2 + 0.0005 3.2005 27. 0.042 + 0.055 0.097
6. 4 + 5.3 9.3 28. 2.7 + 12 14.7
7. 0.4 + 5.3 5.7 29. 2.7 + 1.2 3.9
8. 0.04 + 5.3 5.34 30. 2.7 + 0.12 2.82
9. 0.004 + 5.3 5.304 31. 2.7 + 0.012 2.712
10. 0.0004 + 5.3 5.3004 32. 0.27 + 0.012 0.282
11. 4 + 0.53 4.53 33. 0.027 + 0.012 0.039
12. 6 + 0.2 6.2 34. 0.7 + 3 3.7
13. 0.6 + 0.02 0.62 35. 0.7 + 0.3 1
14. 0.06 + 0.2 0.26 36. 0.07 + 0.03 0.1
15. 0.6 + 2 2.6 37. 0.007 + 0.003 0.01
16. 2 + 0.06 2.06 38. 5 + 0.5 5.5
17. 1 + 0.7 1.7 39. 0.5 + 0.5 1
18. 0.1 + 0.07 0.17 40. 0.05 + 0.05 0.1
19. 0.01 + 0.7 0.71 41. 0.005 + 0.005 0.01
20. 0.1 + 7 7.1 42. 0.2 + 8 8.2
21. 1 + 0.07 1.07 43. 0.2 + 0.8 1
22. 0.1 + 0.7 0.8 44. 0.02 + 0.08 0.1
6β8 Xβ’X
Fluency Support NYS COMMON CORE MATHEMATICS CURRICULUM
Fluency Support for Grades 6β8 Date: 4/2/15
38
Β© 2014 Common Core, Inc. Some rights reserved. commoncore.org This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Addition of Decimals II β Round 1
Directions: Evaluate each expression.
1. 2.5 + 4 23. 4.5 + 3.1
2. 2.5 + 0.4 24. 4.5 + 0.31
3. 2.5 + 0.04 25. 4.5 + 0.031
4. 2.5 + 0.004 26. 0.45 + 0.031
5. 2.5 + 0.0004 27. 0.045 + 0.031
6. 6 + 1.3 28. 12 + 0.36
7. 0.6 + 1.3 29. 1.2 + 3.6
8. 0.06 + 1.3 30. 1.2 + 0.36
9. 0.006 + 1.3 31. 1.2 + 0.036
10. 0.0006 + 1.3 32. 0.12 + 0.036
11. 0.6 + 13 33. 0.012 + 0.036
12. 7 + 0.2 34. 0.7 + 3
13. 0.7 + 0.02 35. 0.7 + 0.3
14. 0.07 + 0.2 36. 0.07 + 0.03
15. 0.7 + 2 37. 0.007 + 0.003
16. 7 + 0.02 38. 5 + 0.5
17. 6 + 0.3 39. 0.5 + 0.5
18. 0.6 + 0.03 40. 0.05 + 0.05
19. 0.06 + 0.3 41. 0.005 + 0.005
20. 0.6 + 3 42. 0.11 + 19
21. 6 + 0.03 43. 1.1 + 1.9
22. 0.6 + 0.3 44. 0.11 + 0.19
Number Correct: ______
6β8 Xβ’X
Fluency Support NYS COMMON CORE MATHEMATICS CURRICULUM
Fluency Support for Grades 6β8 Date: 4/2/15
39
Β© 2014 Common Core, Inc. Some rights reserved. commoncore.org This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Addition of Decimals II β Round 1 [KEY]
Directions: Evaluate each expression.
1. 2.5 + 4 6.5 23. 4.5 + 3.1 7.6
2. 2.5 + 0.4 2.9 24. 4.5 + 0.31 4.81
3. 2.5 + 0.04 2.54 25. 4.5 + 0.031 4.531
4. 2.5 + 0.004 2.504 26. 0.45 + 0.031 0.481
5. 2.5 + 0.0004 2.5004 27. 0.045 + 0.031 0.076
6. 6 + 1.3 7.3 28. 12 + 0.36 12.36
7. 0.6 + 1.3 1.9 29. 1.2 + 3.6 4.8
8. 0.06 + 1.3 1.36 30. 1.2 + 0.36 1.56
9. 0.006 + 1.3 1.306 31. 1.2 + 0.036 1.236
10. 0.0006 + 1.3 1.3006 32. 0.12 + 0.036 0.156
11. 0.6 + 13 13.6 33. 0.012 + 0.036 0.038
12. 7 + 0.2 7.2 34. 0.7 + 3 3.7
13. 0.7 + 0.02 0.72 35. 0.7 + 0.3 1
14. 0.07 + 0.2 0.27 36. 0.07 + 0.03 0.1
15. 0.7 + 2 2.7 37. 0.007 + 0.003 0.01
16. 7 + 0.02 7.02 38. 5 + 0.5 5.5
17. 6 + 0.3 6.3 39. 0.5 + 0.5 1
18. 0.6 + 0.03 0.63 40. 0.05 + 0.05 0.1
19. 0.06 + 0.3 0.36 41. 0.005 + 0.005 0.01
20. 0.6 + 3 3.6 42. 0.11 + 19 19.11
21. 6 + 0.03 6.03 43. 1.1 + 1.9 3
22. 0.6 + 0.3 0.9 44. 0.11 + 0.19 0.3
6β8 Xβ’X
Fluency Support NYS COMMON CORE MATHEMATICS CURRICULUM
Fluency Support for Grades 6β8 Date: 4/2/15
40
Β© 2014 Common Core, Inc. Some rights reserved. commoncore.org This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Addition of Decimals II β Round 2
Directions: Evaluate each expression.
1. 7.4 + 3 23. 3.6 + 2.3
2. 7.4 + 0.3 24. 3.6 + 0.23
3. 7.4 + 0.03 25. 3.6 + 0.023
4. 7.4 + 0.003 26. 0.36 + 0.023
5. 7.4 + 0.0003 27. 0.036 + 0.023
6. 6 + 2.2 28. 0.13 + 56
7. 0.6 + 2.2 29. 1.3 + 5.6
8. 0.06 + 2.2 30. 1.3 + 0.56
9. 0.006 + 2.2 31. 1.3 + 0.056
10. 0.0006 + 2.2 32. 0.13 + 0.056
11. 0.6 + 22 33. 0.013 + 0.056
12. 7 + 0.8 34. 2 + 0.8
13. 0.7 + 0.08 35. 0.2 + 0.8
14. 0.07 + 0.8 36. 0.02 + 0.08
15. 0.7 + 8 37. 0.002 + 0.008
16. 7 + 0.08 38. 0.16 + 14
17. 5 + 0.4 39. 1.6 + 1.4
18. 0.5 + 0.04 40. 0.16 + 0.14
19. 0.05 + 0.4 41. 0.016 + 0.014
20. 0.5 + 4 42. 15 + 0.15
21. 5 + 0.04 43. 1.5 + 1.5
22. 5 + 0.4 44. 0.15 + 0.15
Number Correct: ______
Improvement: ______
6β8 Xβ’X
Fluency Support NYS COMMON CORE MATHEMATICS CURRICULUM
Fluency Support for Grades 6β8 Date: 4/2/15
41
Β© 2014 Common Core, Inc. Some rights reserved. commoncore.org This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Addition of Decimals II β Round 2 [KEY]
Directions: Evaluate each expression.
1. 7.4 + 3 10.4 23. 3.6 + 2.3 5.9
2. 7.4 + 0.3 7.7 24. 3.6 + 0.23 3.83
3. 7.4 + 0.03 7.43 25. 3.6 + 0.023 3.623
4. 7.4 + 0.003 7.403 26. 0.36 + 0.023 0.383
5. 7.4 + 0.0003 7.4003 27. 0.036 + 0.023 0.059
6. 6 + 2.2 8.2 28. 0.13 + 56 56.13
7. 0.6 + 2.2 2.8 29. 1.3 + 5.6 6.9
8. 0.06 + 2.2 2.26 30. 1.3 + 0.56 1.86
9. 0.006 + 2.2 2.206 31. 1.3 + 0.056 1.356
10. 0.0006 + 2.2 2.2006 32. 0.13 + 0.056 0.186
11. 0.6 + 22 22.6 33. 0.013 + 0.056 0.069
12. 7 + 0.8 7.8 34. 2 + 0.8 2.8
13. 0.7 + 0.08 0.78 35. 0.2 + 0.8 1
14. 0.07 + 0.8 0.87 36. 0.02 + 0.08 0.1
15. 0.7 + 8 8.7 37. 0.002 + 0.008 0.01
16. 7 + 0.08 7.08 38. 0.16 + 14 14.16
17. 5 + 0.4 5.4 39. 1.6 + 1.4 3
18. 0.5 + 0.04 0.54 40. 0.16 + 0.14 0.3
19. 0.05 + 0.4 0.45 41. 0.016 + 0.014 0.03
20. 0.5 + 4 4.5 42. 15 + 0.15 15.15
21. 5 + 0.04 5.04 43. 1.5 + 1.5 3
22. 5 + 0.4 5.4 44. 0.15 + 0.15 0.3
6β8 Xβ’X
Fluency Support NYS COMMON CORE MATHEMATICS CURRICULUM
Fluency Support for Grades 6β8 Date: 4/2/15
42
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Subtraction of Decimals
Progression of Exercises
1. 49.5 β 32.1 =
ππ. π
2. 7.48 β 2.26 =
π. ππ
3. 116.32 β 42.07 =
ππ. ππ
4. 128.43 β 87.3 =
ππ. ππ
5. 239.5 β 102.37 =
πππ. ππ
6. 448.9 β 329.18 =
πππ. ππ
7. 134.25 β 103.17 =
ππ. ππ
8. 187.49 β 21 =
πππ. ππ
9. 336.91 β 243.38 =
ππ. ππ
10. 323.2 β 38.74 =
πππ. ππ
6β8 Xβ’X
Fluency Support NYS COMMON CORE MATHEMATICS CURRICULUM
Fluency Support for Grades 6β8 Date: 4/2/15
43
Β© 2014 Common Core, Inc. Some rights reserved. commoncore.org This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Subtraction of Decimals β Round 1
Directions: Evaluate each expression.
1. 55 β 50 23. 9.9 β 5
2. 55 β 5 24. 9.9 β 0.5
3. 5.5 β 5 25. 0.99 β 0.5
4. 5.5 β 0.5 26. 0.99 β 0.05
5. 88 β 80 27. 4.7 β 2
6. 88 β 8 28. 4.7 β 0.2
7. 8.8 β 8 29. 0.47 β 0.2
8. 8.8 β 0.8 30. 0.47 β 0.02
9. 33 β 30 31. 8.4 β 1
10. 33 β 3 32. 8.4 β 0.1
11. 3.3 β 3 33. 0.84 β 0.1
12. 1 β 0.3 34. 7.2 β 5
13. 1 β 0.03 35. 7.2 β 0.5
14. 1 β 0.003 36. 0.72 β 0.5
15. 0.1 β 0.03 37. 0.72 β 0.05
16. 4 β 0.8 38. 8.6 β 7
17. 4 β 0.08 39. 8.6 β 0.7
18. 4 β 0.008 40. 0.86 β 0.7
19. 0.4 β 0.08 41. 0.86 β 0.07
20. 9 β 0.4 42. 5.1 β 4
21. 9 β 0.04 43. 5.1 β 0.4
22. 9 β 0.004 44. 0.51 β 0.4
Number Correct: ______
6β8 Xβ’X
Fluency Support NYS COMMON CORE MATHEMATICS CURRICULUM
Fluency Support for Grades 6β8 Date: 4/2/15
44
Β© 2014 Common Core, Inc. Some rights reserved. commoncore.org This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Subtraction of Decimals β Round 1 [KEY]
Directions: Evaluate each expression.
1. 55 β 50 5 23. 9.9 β 5 4.9
2. 55 β 5 50 24. 9.9 β 0.5 9.4
3. 5.5 β 5 0.5 25. 0.99 β 0.5 0.49
4. 5.5 β 0.5 5 26. 0.99 β 0.05 0.94
5. 88 β 80 8 27. 4.7 β 2 2.7
6. 88 β 8 80 28. 4.7 β 0.2 4.5
7. 8.8 β 8 0.8 29. 0.47 β 0.2 0.27
8. 8.8 β 0.8 8 30. 0.47 β 0.02 0.45
9. 33 β 30 3 31. 8.4 β 1 7.4
10. 33 β 3 30 32. 8.4 β 0.1 8.3
11. 3.3 β 3 0.3 33. 0.84 β 0.1 0.74
12. 1 β 0.3 0.7 34. 7.2 β 5 2.2
13. 1 β 0.03 0.97 35. 7.2 β 0.5 6.7
14. 1 β 0.003 0.997 36. 0.72 β 0.5 0.22
15. 0.1 β 0.03 0.07 37. 0.72 β 0.05 0.67
16. 4 β 0.8 3.2 38. 8.6 β 7 1.6
17. 4 β 0.08 3.92 39. 8.6 β 0.7 7.9
18. 4 β 0.008 3.992 40. 0.86 β 0.7 0.16
19. 0.4 β 0.08 0.32 41. 0.86 β 0.07 0.79
20. 9 β 0.4 8.6 42. 5.1 β 4 4.1
21. 9 β 0.04 8.96 43. 5.1 β 0.4 4.7
22. 9 β 0.004 8.996 44. 0.51 β 0.4 0.41
6β8 Xβ’X
Fluency Support NYS COMMON CORE MATHEMATICS CURRICULUM
Fluency Support for Grades 6β8 Date: 4/2/15
45
Β© 2014 Common Core, Inc. Some rights reserved. commoncore.org This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Subtraction of Decimals β Round 2
Directions: Evaluate each expression.
1. 66 β 60 23. 6.8 β 4
2. 66 β 6 24. 6.8 β 0.4
3. 6.6 β 6 25. 0.68 β 0.4
4. 6.6 β 0.6 26. 0.68 β 0.04
5. 99 β 90 27. 7.3 β 1
6. 99 β 9 28. 7.3 β 0.1
7. 9.9 β 9 29. 0.73 β 0.1
8. 9.9 β 0.9 30. 0.73 β 0.01
9. 22 β 20 31. 9.5 β 2
10. 22 β 2 32. 9.5 β 0.2
11. 2.2 β 2 33. 0.95 β 0.2
12. 3 β 0.4 34. 8.3 β 5
13. 3 β 0.04 35. 8.3 β 0.5
14. 3 β 0.004 36. 0.83 β 0.5
15. 0.3 β 0.04 37. 0.83 β 0.05
16. 8 β 0.2 38. 7.2 β 4
17. 8 β 0.02 39. 7.2 β 0.4
18. 8 β 0.002 40. 0.72 β 0.4
19. 0.8 β 0.02 41. 0.72 β 0.04
20. 5 β 0.1 42. 9.3 β 7
21. 5 β 0.01 43. 9.3 β 0.7
22. 5 β 0.001 44. 0.93 β 0.7
Number Correct: ______
Improvement: ______
6β8 Xβ’X
Fluency Support NYS COMMON CORE MATHEMATICS CURRICULUM
Fluency Support for Grades 6β8 Date: 4/2/15
46
Β© 2014 Common Core, Inc. Some rights reserved. commoncore.org This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Subtraction of Decimals β Round 2 [KEY]
Directions: Evaluate each expression.
1. 66 β 60 6 23. 6.8 β 4 2.8
2. 66 β 6 60 24. 6.8 β 0.4 6.4
3. 6.6 β 6 0.6 25. 0.68 β 0.4 0.28
4. 6.6 β 0.6 6 26. 0.68 β 0.04 0.64
5. 99 β 90 9 27. 7.3 β 1 6.3
6. 99 β 9 90 28. 7.3 β 0.1 7.2
7. 9.9 β 9 0.9 29. 0.73 β 0.1 0.63
8. 9.9 β 0.9 9 30. 0.73 β 0.01 0.72
9. 22 β 20 2 31. 9.5 β 2 7.5
10. 22 β 2 20 32. 9.5 β 0.2 9.3
11. 2.2 β 2 0.2 33. 0.95 β 0.2 0.75
12. 3 β 0.4 2.6 34. 8.3 β 5 3.3
13. 3 β 0.04 2.96 35. 8.3 β 0.5 7.8
14. 3 β 0.004 2.996 36. 0.83 β 0.5 0.33
15. 0.3 β 0.04 0.26 37. 0.83 β 0.05 0.78
16. 8 β 0.2 7.8 38. 7.2 β 4 3.2
17. 8 β 0.02 7.98 39. 7.2 β 0.4 6.8
18. 8 β 0.002 7.998 40. 0.72 β 0.4 0.32
19. 0.8 β 0.02 0.78 41. 0.72 β 0.04 0.68
20. 5 β 0.1 4.9 42. 9.3 β 7 2.3
21. 5 β 0.01 4.99 43. 9.3 β 0.7 8.6
22. 5 β 0.001 4.999 44. 0.93 β 0.7 0.23
6β8 Xβ’X
Fluency Support NYS COMMON CORE MATHEMATICS CURRICULUM
Fluency Support for Grades 6β8 Date: 4/2/15
47
Β© 2014 Common Core, Inc. Some rights reserved. commoncore.org This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Multiplication of Decimals
Progression of Exercises
1. 0.5 Γ 0.5 =
π. ππ
2. 0.6 Γ 0.6 =
π. ππ
3. 0.7 Γ 0.7 =
π. ππ
4. 0.5 Γ 0.6 =
π. π
5. 1.5 Γ 1.5 =
π. ππ
6. 2.5 Γ 2.5 =
π. ππ
7. 0.25 Γ 0.25 =
π. ππππ
8. 0.1 Γ 0.1 =
π. ππ
9. 0.1 Γ 123.4 =
ππ. ππ
10. 0.01 Γ 123.4 =
π. πππ
6β8 Xβ’X
Fluency Support NYS COMMON CORE MATHEMATICS CURRICULUM
Fluency Support for Grades 6β8 Date: 4/2/15
48
Β© 2014 Common Core, Inc. Some rights reserved. commoncore.org This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Multiplication of Decimals β Round 1
Directions: Evaluate each expression.
1. 5 Γ 1 23. 5 Γ 3
2. 5 Γ 0.1 24. 5 Γ 0.3
3. 5 Γ 0.01 25. 0.5 Γ 3
4. 5 Γ 0.001 26. 0.5 Γ 0.3
5. 4 Γ 2 27. 9 Γ 2
6. 4 Γ 0.2 28. 9 Γ 0.2
7. 4 Γ 0.02 29. 0.9 Γ 2
8. 4 Γ 0.002 30. 0.9 Γ 0.2
9. 3 Γ 3 31. 4 Γ 4
10. 3 Γ 0.3 32. 4 Γ 0.4
11. 3 Γ 0.03 33. 0.4 Γ 0.4
12. 0.1 Γ 0.8 34. 0.8 Γ 0.6
13. 0.01 Γ 0.8 35. 0.8 Γ 0.06
14. 0.1 Γ 0.08 36. 0.8 Γ 0.006
15. 0.01 Γ 0.08 37. 0.08 Γ 0.006
16. 0.3 Γ 0.2 38. 0.7 Γ 0.9
17. 0.03 Γ 0.2 39. 0.07 Γ 0.9
18. 0.3 Γ 0.02 40. 0.007 Γ 0.9
19. 0.03 Γ 0.02 41. 0.007 Γ 0.09
20. 0.2 Γ 0.2 42. 1.2 Γ 0.3
21. 0.02 Γ 0.2 43. 1.2 Γ 0.03
22. 0.2 Γ 0.02 44. 1.2 Γ 0.003
Number Correct: ______
6β8 Xβ’X
Fluency Support NYS COMMON CORE MATHEMATICS CURRICULUM
Fluency Support for Grades 6β8 Date: 4/2/15
49
Β© 2014 Common Core, Inc. Some rights reserved. commoncore.org This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Multiplication of Decimals β Round 1 [KEY]
Directions: Evaluate each expression.
1. 5 Γ 1 5 23. 5 Γ 3 15
2. 5 Γ 0.1 0.5 24. 5 Γ 0.3 1.5
3. 5 Γ 0.01 0.05 25. 0.5 Γ 3 1.5
4. 5 Γ 0.001 0.005 26. 0.5 Γ 0.3 0.15
5. 4 Γ 2 8 27. 9 Γ 2 18
6. 4 Γ 0.2 0.8 28. 9 Γ 0.2 1.8
7. 4 Γ 0.02 0.08 29. 0.9 Γ 2 1.8
8. 4 Γ 0.002 0.008 30. 0.9 Γ 0.2 0.18
9. 3 Γ 3 9 31. 4 Γ 4 16
10. 3 Γ 0.3 0.9 32. 4 Γ 0.4 1.6
11. 3 Γ 0.03 0.09 33. 0.4 Γ 0.4 0.16
12. 0.1 Γ 0.8 0.08 34. 0.8 Γ 0.6 0.48
13. 0.01 Γ 0.8 0.008 35. 0.8 Γ 0.06 0.048
14. 0.1 Γ 0.08 0.008 36. 0.8 Γ 0.006 0.0048
15. 0.01 Γ 0.08 0.0008 37. 0.08 Γ 0.006 0.00048
16. 0.3 Γ 0.2 0.06 38. 0.7 Γ 0.9 0.63
17. 0.03 Γ 0.2 0.006 39. 0.07 Γ 0.9 0.063
18. 0.3 Γ 0.02 0.006 40. 0.007 Γ 0.9 0.0063
19. 0.03 Γ 0.02 0.0006 41. 0.007 Γ 0.09 0.00063
20. 0.2 Γ 0.2 0.04 42. 1.2 Γ 0.3 0.36
21. 0.02 Γ 0.2 0.004 43. 1.2 Γ 0.03 0.036
22. 0.2 Γ 0.02 0.004 44. 1.2 Γ 0.003 0.0036
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Multiplication of Decimals β Round 2
Directions: Evaluate each expression.
1. 9 Γ 1 23. 3 Γ 4
2. 0.9 Γ 1 24. 3 Γ 0.4
3. 0.09 Γ 1 25. 0.3 Γ 4
4. 0.009 Γ 1 26. 0.3 Γ 0.4
5. 2 Γ 2 27. 7 Γ 7
6. 2 Γ 0.2 28. 7 Γ 0.7
7. 2 Γ 0.02 29. 0.7 Γ 7
8. 2 Γ 0.002 30. 0.7 Γ 0.7
9. 3 Γ 2 31. 2 Γ 8
10. 0.3 Γ 2 32. 2 Γ 0.8
11. 0.03 Γ 2 33. 0.2 Γ 0.8
12. 0.7 Γ 0.1 34. 0.6 Γ 0.5
13. 0.07 Γ 0.1 35. 0.6 Γ 0.05
14. 0.7 Γ 0.01 36. 0.6 Γ 0.005
15. 0.07 Γ 0.01 37. 0.06 Γ 0.005
16. 0.2 Γ 0.4 38. 0.9 Γ 0.9
17. 0.02 Γ 0.4 39. 0.09 Γ 0.9
18. 0.2 Γ 0.04 40. 0.009 Γ 0.9
19. 0.02 Γ 0.04 41. 0.009 Γ 0.09
20. 0.1 Γ 0.1 42. 1.1 Γ 0.5
21. 0.01 Γ 0.1 43. 1.1 Γ 0.05
22. 0.1 Γ 0.01 44. 1.1 Γ 0.005
Number Correct: ______
Improvement: ______
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Multiplication of Decimals β Round 2 [KEY]
Directions: Evaluate each expression.
1. 9 Γ 1 9 23. 3 Γ 4 12
2. 0.9 Γ 1 0.9 24. 3 Γ 0.4 1.2
3. 0.09 Γ 1 0.09 25. 0.3 Γ 4 1.2
4. 0.009 Γ 1 0.009 26. 0.3 Γ 0.4 0.12
5. 2 Γ 2 4 27. 7 Γ 7 49
6. 2 Γ 0.2 0.4 28. 7 Γ 0.7 4.9
7. 2 Γ 0.02 0.04 29. 0.7 Γ 7 4.9
8. 2 Γ 0.002 0.004 30. 0.7 Γ 0.7 0.49
9. 3 Γ 2 6 31. 2 Γ 8 16
10. 0.3 Γ 2 0.6 32. 2 Γ 0.8 1.6
11. 0.03 Γ 2 0.06 33. 0.2 Γ 0.8 0.16
12. 0.7 Γ 0.1 0.07 34. 0.6 Γ 0.5 0.3
13. 0.07 Γ 0.1 0.007 35. 0.6 Γ 0.05 0.03
14. 0.7 Γ 0.01 0.007 36. 0.6 Γ 0.005 0.003
15. 0.07 Γ 0.01 0.0007 37. 0.06 Γ 0.005 0.0003
16. 0.2 Γ 0.4 0.08 38. 0.9 Γ 0.9 0.81
17. 0.02 Γ 0.4 0.008 39. 0.09 Γ 0.9 0.81
18. 0.2 Γ 0.04 0.008 40. 0.009 Γ 0.9 0.0081
19. 0.02 Γ 0.04 0.0008 41. 0.009 Γ 0.09 0.00081
20. 0.1 Γ 0.1 0.01 42. 1.1 Γ 0.5 0.55
21. 0.01 Γ 0.1 0.001 43. 1.1 Γ 0.05 0.055
22. 0.1 Γ 0.01 0.001 44. 1.1 Γ 0.005 0.0055
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Multiplication of Decimals IIβRound 1
Directions: Determine the products of the decimals.
1. 4.5 Γ 3 19. 3.5 Γ 4.1
2. 7.2 Γ 8 20. 9.3 Γ 1.7
3. 9.4 Γ 6 21. 10.4 Γ 7.6
4. 10.2 Γ 7 22. 2.7 Γ 8.3
5. 8.3 Γ 4 23. 1.8 Γ 7.8
6. 5.8 Γ 2 24. 7.5 Γ 10.1
7. 7.1 Γ 9 25. 7.2 Γ 6.3
8. 5.9 Γ 10 26. 1.9 Γ 8.3
9. 3.4 Γ 3 27. 9.8 Γ 5.1
10. 3.2 Γ 4 28. 18.2 Γ 12
11. 6 Γ 2.8 29. 13.4 Γ 22
12. 9.7 Γ 3 30. 92.3 Γ 45
13. 8 Γ 10.2 31. 86.1 Γ 16
14. 4 Γ 8.9 32. 29.7 Γ 8.2
15. 3.9 Γ 7 33. 56.8 Γ 9.5
16. 6 Γ 5.5 34. 110.3 Γ 20.2
17. 1.8 Γ 8 35. 256.6 Γ 54.9
18. 9 Γ 2.3 36. 312.8 Γ 16.5
Number Correct: ______
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Multiplication of Decimals IIβRound 1 [KEY]
Directions: Determine the products of the decimals.
1. 4.5 Γ 3 ππ. π 19. 3.5 Γ 4.1 ππ. ππ
2. 7.2 Γ 8 ππ. π 20. 9.3 Γ 1.7 ππ. ππ
3. 9.4 Γ 6 ππ. π 21. 10.4 Γ 7.6 ππ. ππ
4. 10.2 Γ 7 ππ. π 22. 2.7 Γ 8.3 ππ. ππ
5. 8.3 Γ 4 ππ. π 23. 1.8 Γ 7.8 ππ. ππ
6. 5.8 Γ 2 ππ. π 24. 7.5 Γ 10.1 ππ. ππ
7. 7.1 Γ 9 ππ. π 25. 7.2 Γ 6.3 ππ. ππ
8. 5.9 Γ 10 ππ 26. 1.9 Γ 8.3 ππ. ππ
9. 3.4 Γ 3 ππ. π 27. 9.8 Γ 5.1 ππ. ππ
10. 3.2 Γ 4 ππ. π 28. 18.2 Γ 12 πππ. π
11. 6 Γ 2.8 ππ. π 29. 13.4 Γ 22 πππ. π
12. 9.7 Γ 3 ππ. π 30. 92.3 Γ 45 ππππ. π
13. 8 Γ 10.2 ππ. π 31. 86.1 Γ 16 ππππ. π
14. 4 Γ 8.9 ππ. π 32. 29.7 Γ 8.2 πππ. ππ
15. 3.9 Γ 7 ππ. π 33. 56.8 Γ 9.5 πππ. π
16. 6 Γ 5.5 ππ. π 34. 110.3 Γ 20.2 ππππ. ππ
17. 1.8 Γ 8 ππ. π 35. 256.6 Γ 54.9 πππππ. ππ
18. 9 Γ 2.3 ππ. π 36. 312.8 Γ 16.5 ππππ. π
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Multiplication of Decimals IIβRound 2
Directions: Determine the products of the decimals.
1. 3.7 Γ 8 19. 4.6 Γ 5.2
2. 9.2 Γ 10 20. 6.8 Γ 1.9
3. 2.1 Γ 3 21. 7.8 Γ 10.4
4. 4.8 Γ 9 22. 3.8 Γ 3.9
5. 3.3 Γ 5 23. 9.3 Γ 4.2
6. 7.4 Γ 4 24. 1.4 Γ 9.5
7. 8.1 Γ 9 25. 9.4 Γ 2.7
8. 1.9 Γ 2 26. 5.6 Γ 4.2
9. 5.6 Γ 7 27. 8.6 Γ 3.1
10. 3.6 Γ 8 28. 14.5 Γ 19
11. 4 Γ 9.8 29. 33 Γ 10.2
12. 5 Γ 8.7 30. 51 Γ 32.4
13. 1.4 Γ 7 31. 45 Γ 17.6
14. 3 Γ 10.2 32. 15.2 Γ 6.7
15. 2.8 Γ 6 33. 39.5 Γ 8.4
16. 3.9 Γ 9 34. 96.8 Γ 31.7
17. 8.2 Γ 6 35. 189.1 Γ 72.9
18. 4.5 Γ 9 36. 302.4 Γ 13.1
Number Correct: ______
Improvement: ______
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Multiplication of Decimals IIβRound 2 [KEY]
Directions: Determine the products of the decimals.
1. 3.7 Γ 8 ππ. π 19. 4.6 Γ 5.2 ππ. ππ
2. 9.2 Γ 10 ππ 20. 6.8 Γ 1.9 ππ. ππ
3. 2.1 Γ 3 π. π 21. 7.8 Γ 10.4 ππ. ππ
4. 4.8 Γ 9 ππ. π 22. 3.8 Γ 3.9 ππ. ππ
5. 3.3 Γ 5 ππ. π 23. 9.4 Γ 4.2 ππ. ππ
6. 7.4 Γ 4 ππ. π 24. 1.4 Γ 9.5 ππ. π
7. 8.1 Γ 9 ππ. π 25. 9.4 Γ 2.7 ππ. ππ
8. 1.9 Γ 2 π. π 26. 5.6 Γ 4.2 ππ. ππ
9. 5.6 Γ 7 ππ. π 27. 8.6 Γ 3.1 ππ. ππ
10. 3.6 Γ 8 ππ. π 28. 14.5 Γ 19 πππ. π
11. 4 Γ 9.8 ππ. π 29. 33 Γ 10.2 πππ. π
12. 5 Γ 8.7 ππ. π 30. 51 Γ 32.4 ππππ. π
13. 1.4 Γ 7 π. π 31. 45 Γ 17.6 πππ. π
14. 3 Γ 10.2 ππ. π 32. 15.2 Γ 6.7 πππ. ππ
15. 2.8 Γ 6 ππ. π 33. 39.5 Γ 8.4 πππ. π
16. 3.9 Γ 9 ππ. π 34. 96.8 Γ 31.7 ππππ. ππ
17. 8.2 Γ 6 ππ. π 35. 189.1 Γ 72.9 πππππ. ππ
18. 4.5 Γ 9 ππ. π 36. 302.4 Γ 13.1 ππππ. ππ
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Greatest Common FactorβRound 1
Directions: Determine the greatest common factor of each pair of numbers.
1. GCF of 10 and 50 16. GCF of 45 and 72
2. GCF of 5 and 35 17. GCF of 28 and 48
3. GCF of 3 and 12 18. GCF of 44 and 77
4. GCF of 8 and 20 19. GCF of 39 and 66
5. GCF of 15 and 35 20. GCF of 64 and 88
6. GCF of 10 and 75 21. GCF of 42 and 56
7. GCF of 9 and 30 22. GCF of 28 and 42
8. GCF of 15 and 33 23. GCF of 13 and 91
9. GCF of 12 and 28 24. GCF of 16 and 84
10. GCF of 16 and 40 25. GCF of 36 and 99
11. GCF of 24 and 32 26. GCF of 39 and 65
12. GCF of 35 and 49 27. GCF of 27 and 87
13. GCF of 45 and 60 28. GCF of 28 and 70
14. GCF of 48 and 72 29. GCF of 26 and 91
15. GCF of 50 and 42 30. GCF of 34 and 51
Number Correct: ______
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Greatest Common FactorβRound 1 [KEY]
Directions: Determine the greatest common factor of each pair of numbers.
1. GCF of 10 and 50 ππ 16. GCF of 45 and 72 π
2. GCF of 5 and 35 π 17. GCF of 28 and 48 π
3. GCF of 3 and 12 π 18. GCF of 44 and 77 ππ
4. GCF of 8 and 20 π 19. GCF of 39 and 66 π
5. GCF of 15 and 35 π 20. GCF of 64 and 88 π
6. GCF of 10 and 75 π 21. GCF of 42 and 56 ππ
7. GCF of 9 and 30 π 22. GCF of 28 and 42 ππ
8. GCF of 15 and 33 π 23. GCF of 13 and 91 ππ
9. GCF of 12 and 28 π 24. GCF of 16 and 84 π
10. GCF of 16 and 40 π 25. GCF of 36 and 99 π
11. GCF of 24 and 32 π 26. GCF of 39 and 65 ππ
12. GCF of 35 and 49 π 27. GCF of 27 and 87 π
13. GCF of 45 and 60 ππ 28. GCF of 28 and 70 ππ
14. GCF of 48 and 72 ππ 29. GCF of 26 and 91 ππ
15. GCF of 50 and 42 π 30. GCF of 34 and 51 ππ
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Greatest Common FactorβRound 2
Directions: Determine the greatest common factor of each pair of numbers.
1. GCF of 20 and 80 16. GCF of 33 and 99
2. GCF of 10 and 70 17. GCF of 38 and 76
3. GCF of 9 and 36 18. GCF of 26 and 65
4. GCF of 12 and 24 19. GCF of 39 and 48
5. GCF of 15 and 45 20. GCF of 72 and 88
6. GCF of 10 and 95 21. GCF of 21 and 56
7. GCF of 9 and 45 22. GCF of 28 and 52
8. GCF of 18 and 33 23. GCF of 51 and 68
9. GCF of 12 and 32 24. GCF of 48 and 84
10. GCF of 16 and 56 25. GCF of 21 and 63
11. GCF of 40 and 72 26. GCF of 64 and 80
12. GCF of 35 and 63 27. GCF of 36 and 90
13. GCF of 30 and 75 28. GCF of 28 and 98
14. GCF of 42 and 72 29. GCF of 39 and 91
15. GCF of 30 and 28 30. GCF of 38 and 95
Number Correct: ______
Improvement: ______
6β8 Xβ’X
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Greatest Common FactorβRound 2 [KEY]
Directions: Determine the greatest common factor of each pair of numbers.
1. GCF of 20 and 80 ππ 16. GCF of 33 and 99 ππ
2. GCF of 10 and 70 ππ 17. GCF of 38 and 76 ππ
3. GCF of 9 and 36 π 18. GCF of 26 and 65 ππ
4. GCF of 12 and 24 ππ 19. GCF of 39 and 48 π
5. GCF of 15 and 45 ππ 20. GCF of 72 and 88 π
6. GCF of 10 and 95 π 21. GCF of 21 and 56 π
7. GCF of 9 and 45 π 22. GCF of 28 and 52 π
8. GCF of 18 and 33 π 23. GCF of 51 and 68 ππ
9. GCF of 12 and 32 π 24. GCF of 48 and 84 ππ
10. GCF of 16 and 56 π 25. GCF of 21 and 63 ππ
11. GCF of 40 and 72 π 26. GCF of 64 and 80 ππ
12. GCF of 35 and 63 π 27. GCF of 36 and 90 ππ
13. GCF of 30 and 75 ππ 28. GCF of 28 and 98 ππ
14. GCF of 42 and 72 π 29. GCF of 39 and 91 ππ
15. GCF of 30 and 28 π 30. GCF of 38 and 95 ππ
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Rational Numbers: Inequality StatementsβRound 1
Directions: Work in numerical order to answer Problems 1β33. Arrange each set of numbers in order according to the
inequality symbols.
1. < <
1 , β1 , 0
12. > >
7 , β6 , 6
23. > >
25 , ΒΎ , β ΒΎ 2. > >
1 , β1 , 0
13. > >
17 , 4 , 16
24. < <
25 , ΒΎ , β ΒΎ 3. < <
3 Β½ , β3 Β½ , 0
14. < <
17 , 4 , 16
25. > >
2.2 , 2.3 , 2.4 4. > >
3 Β½ , β3 Β½ , 0
15. < <
0 , 12 , β11
26. > >
1.2 , 1.3 , 1.4 5. > >
1 , β Β½ , Β½
16. > >
0 , 12 , β11
27. > >
0.2 , 0.3 , 0.4 6. < <
1 , β Β½ , Β½
17. > >
1 , ΒΌ , Β½
28. > >
β0.5 , β 1 , β 0.6 7. < <
β3 , β4 , β5
18. < <
1 , ΒΌ , Β½
29. < <
β0.5 , β1 , β0.6 8. < < β13 , β14 , β15
19. < <
β Β½ , Β½ , 0
30. < <
β8 , β9 , 8 9. > >
β13 , β14 , β15
20. > >
βΒ½ , Β½ , 0
31. < <
β18 , β19 , β2 10. < <
β ΒΌ , β1 , 0
21. < <
50 , β10 , 0
32. > >
β2 , β 3 , 1 11. > >
βΒΌ , β1 , 0
22. 3 < <
β50 , 10 , 0
33. < <
β2 , β 3 , 1
Number Correct: ______
6β8 Xβ’X
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Rational Numbers: Inequality StatementsβRound 1 [KEY]
Directions: Work in numerical order to answer Problems 1β33. Arrange each set of numbers in order according to the
inequality symbols.
1. < <
1 , β1 , 0
12. > >
7 , β6 , 6
23. > >
25 , ΒΎ , β ΒΎ 2. > >
1 , β1 , 0
13. > >
17 , 4 , 16
24. < <
25 , ΒΎ , β ΒΎ 3. < <
3 Β½ , β3 Β½ , 0
14. < <
17 , 4 , 16
25. > >
2.2 , 2.3 , 2.4 4. > >
3 Β½ , β3 Β½ , 0
15. < <
0 , 12 , β11
26. > >
1.2 , 1.3 , 1.4 5. > >
1 , β Β½ , Β½
16. > >
0 , 12 , β11
27. > >
0.2 , 0.3 , 0.4 6. < <
1 , β Β½ , Β½
17. > >
1 , ΒΌ , Β½
28. > >
β0.5 , β 1 , β 0.6 7. < <
β3 , β4 , β5
18. < <
1 , ΒΌ , Β½
29. < <
β0.5 , β1 , β0.6 8. < < β13 , β14 , β15
19. < <
β Β½ , Β½ , 0
30. < <
β8 , β9 , 8 9. > >
β13 , β14 , β15
20. > >
βΒ½ , Β½ , 0
31. < <
β18 , β19 , β2 10. < <
β ΒΌ , β1 , 0
21. < <
50 , β10 , 0
32. > >
β2 , β 3 , 1 11. > >
βΒΌ , β1 , 0
22. 3 < <
β50 , 10 , 0
33. < <
β2 , β 3 , 1
βπ π π π π βπ ππ ΒΎ βΒΎ
π
π βπ ππ ππ π βΒΎ ΒΎ ππ
βπ Β½ π π Β½ π ππ ππ π. π π. π π. π
π Β½ π βπ Β½ βππ π βππ π. π π. π π. π
π Β½ βΒ½ ππ π βππ π. π π. π π. π
βΒ½ Β½ π π Β½ ΒΌ βπ. π βπ. π βπ
βπ βπ βπ ΒΌ Β½ 1 βπ βπ. π βπ. π
βππ βππ βππ βΒ½ π Β½ βπ βπ π
βππ βππ βππ Β½ π βΒ½ βππ βππ βπ
βπ βΒΌ π βππ π ππ π βπ βπ
π βΒΌ βπ βππ π ππ βπ βπ π
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Rational Numbers: Inequality StatementsβRound 2
Directions: Work in numerical order to answer Problems 1β33. Arrange each set of numbers in order according to the
inequality symbols.
1. < <
1/7 , β1/7 , 0
12. > >
1 ΒΌ , 1 , 1 Β½
23. > > 1 , 1ΒΎ , β 1ΒΎ
2. > >
1/7 , β1/7 , 0
13. > >
11 ΒΌ , 11 , 11 Β½
24. < <
1 , 1ΒΎ , β 1ΒΎ 3. < < 3/7 , 2/7 , β1/7
14. < <
11 ΒΌ , 11 , 11 Β½
25. > >
β82 , β93 , β104 4. > >
3/7 , 2/7 , β1/7
15. < <
0 , 0.2 , β0.1
26. < <
β82 , β93 , β104 5. > >
β4/5 , 1/5 , β1/5
16. > >
0 , 0.2 , β0.1
27. > >
0.5 , 1 , 0.6 6. < <
β4/5 , 1/5 , β1/5
17. > >
1 , 0.7, 1/10
28. > >
β0.5 , β 1 , β0.6 7. < <
β8/9 , 5/9, 1/9
18. < <
1 , 0.7, 1/10
29. < <
β0.5 , β 1 , β0.6 8. > >
β8/9 , 5/9, 1/9
19. < <
0 , β12 , β12Β½
30. < <
1 , 8 , 9 9. > >
β30 , β10 , β50
20. > >
0 , β12 , β12Β½
31. < <
β1 , β8 , β9 10. < <
β30 , β10 , β50
21. < <
5 , β1 , 0
32. > >
β2 , β3 , β5 11. > >
β40 , β20 , β60
22. < <
β5 , 1 , 0
33. > >
2 , 3 , 5
Number Correct: ______
Improvement: ______
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Rational Numbers: Inequality StatementsβRound 2 [KEY]
Directions: Work in numerical order to answer Problems 1β33. Arrange each set of numbers in order according to the
inequality symbols.
1. < <
1/7 , β1/7 , 0
12. > >
1 ΒΌ , 1 , 1 Β½
23. > > 1 , 1ΒΎ , β 1ΒΎ
2. > >
1/7 , β1/7 , 0
13. > >
11 ΒΌ , 11 , 11 Β½
24. < <
1 , 1ΒΎ , β 1ΒΎ 3. < < 3/7 , 2/7 , β1/7
14. < <
11 ΒΌ , 11 , 11 Β½
25. > >
β82 , β93 , β104 4. > >
3/7 , 2/7 , β1/7
15. < <
0 , 0.2 , β0.1
26. < <
β82 , β93 , β104 5. > >
β4/5 , 1/5 , β1/5
16. > >
0 , 0.2 , β0.1
27. > >
0.5 , 1 , 0.6 6. < <
β4/5 , 1/5 , β1/5
17. > >
1 , 0.7, 1/10
28. > >
β0.5 , β 1 , β0.6 7. < <
β8/9 , 5/9, 1/9
18. < <
1 , 0.7, 1/10
29. < <
β0.5 , β 1 , β0.6 8. > >
β8/9 , 5/9, 1/9
19. < <
0 , β12 , β12Β½
30. < <
1 , 8 , 9 9. > >
β30 , β10 , β50
20. > >
0 , β12 , β12Β½
31. < <
β1 , β8 , β9 10. < <
β30 , β10 , β50
21. < <
5 , β1 , 0
32. > >
β2 , β3 , β5 11. > >
β40 , β20 , β60
22. < <
β5 , 1 , 0
33. > >
2 , 3 , 5
βπ
π π
π
π
π Β½ π ΒΌ π π ΒΎ π βπ ΒΎ
π
π
π βπ
π
ππ Β½ ππ ΒΌ ππ βπ ΒΎ π π ΒΎ
βπ
π
π
π
π
π ππ ππ ΒΌ ππ Β½ βππ βππ βπππ
π
π
π
π
βπ
π
βπ. π π π. π βπππ βππ βππ
π
π
βπ
π
βπ
π
π. π π βπ. π π π. π π. π
βπ
π
βπ
π
π
π
π π
ππ
π. π βπ. π βπ. π βπ
βπ
π
π
π
π
π
π. π π
ππ π βπ βπ. π βπ. π
π
π
π
π
βπ
π
βππ Β½ βππ π π π π
βππ βππ βππ π βππ βππ Β½ βπ βπ βπ
βππ βππ βππ βπ π π βπ βπ βπ
βπ π π π π π βππ βππ βππ
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Addition and Subtraction EquationsβRound 1
Directions: Find the value of π in each equation.
1. π + 4 = 11 18. π β 54 = 37
2. π + 2 = 5 19. 4 + π = 9
3. π + 5 = 8 20. 6 + π = 13
4. π β 7 = 10 21. 2 + π = 31
5. π β 8 = 1 22. 15 = π + 11
6. π β 4 = 2 23. 24 = π + 13
7. π + 12 = 34 24. 32 = π + 28
8. π + 25 = 45 25. 4 = π β 7
9. π + 43 = 89 26. 3 = π β 5
10. π β 20 = 31 27. 12 = π β 14
11. π β 13 = 34 28. 23.6 = π β 7.1
12. π β 45 = 68 29. 14.2 = π β 33.8
13. π + 34 = 41 30. 2.5 = π β 41.8
14. π + 29 = 52 31. 64.9 = π + 23.4
15. π + 37 = 61 32. 72.2 = π + 38.7
16. π β 43 = 63 33. 1.81 = π β 15.13
17. π β 21 = 40 34. 24.68 = π β 56.82
Number Correct: ______
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Addition and Subtraction EquationsβRound 1 [KEY]
Directions: Find the value of π in each equation.
1. π + 4 = 11 π = π 18. π β 54 = 37 π = ππ
2. π + 2 = 5 π = π 19. 4 + π = 9 π = π
3. π + 5 = 8 π = π 20. 6 + π = 13 π = π
4. π β 7 = 10 π = ππ 21. 2 + π = 31 π = ππ
5. π β 8 = 1 π = π 22. 15 = π + 11 π = π
6. π β 4 = 2 π = π 23. 24 = π + 13 π = ππ
7. π + 12 = 34 π = ππ 24. 32 = π + 28 π = π
8. π + 25 = 45 π = ππ 25. 4 = π β 7 π = ππ
9. π + 43 = 89 π = ππ 26. 3 = π β 5 π = π
10. π β 20 = 31 π = ππ 27. 12 = π β 14 π = ππ
11. π β 13 = 34 π = ππ 28. 23.6 = π β 7.1 π = ππ. π
12. π β 45 = 68 π = πππ 29. 14.2 = π β 33.8 π = ππ
13. π + 34 = 41 π = π 30. 2.5 = π β 41.8 π = ππ. π
14. π + 29 = 52 π = ππ 31. 64.9 = π + 23.4 π = ππ. π
15. π + 37 = 61 π = ππ 32. 72.2 = π + 38.7 π = ππ. π
16. π β 43 = 63 π = πππ 33. 1.81 = π β 15.13 π = ππ. ππ
17. π β 21 = 40 π = ππ 34. 24.68 = π β 56.82 π = ππ. π
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Addition and Subtraction EquationsβRound 2
Directions: Find the value of π in each equation.
1. π + 2 = 7 18. 6 = π + 3
2. π + 4 = 10 19. 12 = π + 7
3. π + 8 = 15 20. 24 = π + 16
4. π + 7 = 23 21. 13 = π + 9
5. π + 12 = 16 22. 32 = π β 3
6. π β 5 = 2 23. 22 = π β 12
7. π β 3 = 8 24. 34 = π β 10
8. π β 4 = 12 25. 48 = π + 29
9. π β 14 = 45 26. 21 = π + 17
10. π + 23 = 40 27. 52 = π + 37
11. π + 13 = 31 28. 6
7 = π +
4
7
12. π + 23 = 48 29. 2
3= π β
5
3
13. π + 38 = 52 30. 1
4= π β
8
3
14. π β 14 = 27 31. 5
6= π β
7
12
15. π β 23 = 35 32. 7
8= π β
5
12
16. π β 17 = 18 33. 7
6+ π =
16
3
17. π β 64 = 1 34. 1
3+ π =
13
15
Number Correct: ______
Improvement: ______
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Addition and Subtraction EquationsβRound 2 [KEY]
Directions: Find the value of π in each equation.
1. π + 2 = 7 π = π 18. 6 = π + 3 π = π
2. π + 4 = 10 π = π 19. 12 = π + 7 π = π
3. π + 8 = 15 π = π 20. 24 = π + 16 π = π
4. π + 7 = 23 π = ππ 21. 13 = π + 9 π = π
5. π + 12 = 16 π = π 22. 32 = π β 3 π = ππ
6. π β 5 = 2 π = π 23. 22 = π β 12 π = ππ
7. π β 3 = 8 π = ππ 24. 34 = π β 10 π = ππ
8. π β 4 = 12 π = ππ 25. 48 = π + 29 π = ππ
9. π β 14 = 45 π = ππ 26. 21 = π + 17 π = π
10. π + 23 = 40 π = ππ 27. 52 = π + 37 π = ππ
11. π + 13 = 31 π = ππ 28. 6
7 = π +
4
7 π =
π
π
12. π + 23 = 48 π = ππ 29. 2
3= π β
5
3 π =
π
π
13. π + 38 = 52 π = ππ 30. 1
4= π β
8
3 π =
ππ
ππ
14. π β 14 = 27 π = ππ 31. 5
6= π β
7
12 π =
ππ
ππ
15. π β 23 = 35 π = ππ 32. 7
8= π β
5
12 π =
ππ
ππ
16. π β 17 = 18 π = ππ 33. 7
6+ π =
16
3 π =
ππ
π
17. π β 64 = 1 π = ππ 34. 1
3+ π =
13
15 π =
π
ππ
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Multiplication and Division Equations with Fractions
Progression of Exercises
1. 5π¦ = 35
π = π
2. 3π = 135
π = ππ
3. 12π = 156
π = ππ
4. π
3= 24
π = ππ
5. π₯
7= 42
π = ππ4
6. π
13= 18
π = πππ
7. 2
3π = 6
π = π
8. 3
5π = 9
π = ππ
9. 3
4π¦ = 10
π =ππ
π= ππ
π
π
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10. 5
8π = 9
π =ππ
π= ππ
π
π
11. 3
7β = 13
π =ππ
π= ππ
π
π
12. π
4=
3
5
π =ππ
π= π
π
π
13. π
3=
2
7
π =π
π
14. 2
5π =
3
7
π =ππ
ππ= π
π
ππ
15. 3
4π =
5
8
π =ππ
ππ=
π
π
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Area of Shapes
1.
π¨ = ππ πππ
2.
π¨ = ππ π¦π
3.
π¨ = πππ π’π§π
4.
π¨ = π, πππ ππ¦π
5.
π¨ = ππ πππ
8 ft.
10 ft.
12 m
13 m 5 m
22 in.
22 in.
49 cm
21 cm
12 ft.
10 ft. 8 ft.
6 ft.
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6.
π¨ = πππ π€π¦π
7.
π¨ = πππ π’π§π
8.
π¨ = πππ ππ¦π
9.
π¨ = πππ π¦π
13 km
8 km
12 km
5 km
13 km
5 km
12 km
8 km
4 cm
4 cm
4 cm
4 cm
8 cm
8 cm
8 cm 8 cm
8 cm
8 cm
16 m
36 m 48 m
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10.
π¨ = π, πππ πππ
82 ft.
18 ft.
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Integer AdditionβRound 1
Directions: Determine the sum of the integers, and write it in the column to the right.
1. 8 + (β5) 18. β38 + 25
2. 10 + (β3) 19. β19 + (β11)
3. 2 + (β7) 20. 2 + (β7)
4. 4 + (β11) 21. β23 + (β23)
5. β3 + (β9) 22. 45 + (β32)
6. β12 + (β7) 23. 16 + (β24)
7. β13 + 5 24. β28 + 13
8. β4 + 9 25. β15 + 15
9. 7 + (β7) 26. 12 + (β19)
10. β13 + 13 27. β24 + (β32)
11. 14 + (β20) 28. β18 + (β18)
12. 6 + (β4) 29. 14 + (β26)
13. 10 + (β7) 30. β7 + 8 + (β3)
14. β16 + 9 31. 2 + (β15) + 4
15. β10 + 34 32. β8 + (β19) + (β11)
16. β20 + (β5) 33. 15 + (β12) + 7
17. β18 + 15 34. β28 + 7 + (β7)
Number Correct: ______
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Integer AdditionβRound 1 [KEY]
Directions: Determine the sum of the integers, and write it in the column to the right.
1. 8 + (β5) π 18. β38 + 25 βππ
2. 10 + (β3) π 19. β19 + (β11) βππ
3. 2 + (β7) βπ 20. 2 + (β7) βπ
4. 4 + (β11) βπ 21. β23 + (β23) βππ
5. β3 + (β9) βππ 22. 45 + (β32) ππ
6. β12 + (β7) βππ 23. 16 + (β24) βπ
7. β13 + 5 βπ 24. β28 + 13 βππ
8. β4 + 9 π 25. β15 + 15 π
9. 7 + (β7) π 26. 12 + (β19) βπ
10. β13 + 13 π 27. β24 + (β32) βππ
11. 14 + (β20) βπ 28. β18 + (β18) βππ
12. 6 + (β4) π 29. 14 + (β26) βππ
13. 10 + (β7) π 30. β7 + 8 + (β3) βπ
14. β16 + 9 βπ 31. 2 + (β15) + 4 βπ
15. β10 + 34 ππ 32. β8 + (β19) + (β11) βππ
16. β20 + (β5) βππ 33. 15 + (β12) + 7 ππ
17. β18 + 15 βπ 34. β28 + 7 + (β7) βππ
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Integer AdditionβRound 2
Directions: Determine the sum of the integers, and write it in the column to the right.
1. 5 + (β12) 18. 23 + (β31)
2. 10 + (β6) 19. β26 + (β19)
3. β9 + (β13) 20. 16 + (β37)
4. β12 + 17 21. β21 + 14
5. β15 + 15 22. 33 + (β8)
6. 16 + (β25) 23. β31 + (β13)
7. β12 + (β8) 24. β16 + 16
8. β25 + (β29) 25. 30 + (β43)
9. 28 + (β12) 26. β22 + (β18)
10. β19 + (β19) 27. β43 + 27
11. β17 + 20 28. 38 + (β19)
12. 8 + (β18) 29. β13 + (β13)
13. 13 + (β15) 30. 5 + (β8) + (β3)
14. β10 + (β16) 31. 6 + (β11) + 14
15. 35 + (β35) 32. β17 + 5 + 19
16. 9 + (β14) 33. β16 + (β4) + (β7)
17. β34 + (β27) 34. 8 + (β24) + 12
Number Correct: ______
Improvement: ______
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Integer AdditionβRound 2 [KEY]
Directions: Determine the sum of the integers, and write it in the column to the right.
1. 5 + (β12) βπ 18. 23 + (β31) βπ
2. 10 + (β6) π 19. β26 + (β19) βππ
3. β9 + (β13) βππ 20. 16 + (β37) βππ
4. β12 + 17 π 21. β21 + 14 βπ
5. β15 + 15 π 22. 33 + (β8) ππ
6. 16 + (β25) βπ 23. β31 + (β13) βππ
7. β12 + (β8) βππ 24. β16 + 16 π
8. β25 + (β29) βππ 25. 30 + (β43) βππ
9. 28 + (β12) ππ 26. β22 + (β18) βππ
10. β19 + (β19) βππ 27. β43 + 27 βππ
11. β17 + 20 π 28. 38 + (β19) ππ
12. 8 + (β18) βππ 29. β13 + (β13) βππ
13. 13 + (β15) βπ 30. 5 + (β8) + (β3) βπ
14. β10 + (β16) βππ 31. 6 + (β11) + 14 π
15. 35 + (β35) π 32. β17 + 5 + 19 π
16. 9 + (β14) βπ 33. β16 + (β4) + (β7) βππ
17. β34 + (β27) βππ 34. 8 + (β24) + 12 βπ
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Integer SubtractionβRound 1
Directions: Determine the difference of the integers, and write it in the column to the right.
1. 4 β 2 23. (β6) β 5
2. 4 β 3 24. (β6) β 7
3. 4 β 4 25. (β6) β 9
4. 4 β 5 26. (β14) β 9
5. 4 β 6 27. (β25) β 9
6. 4 β 9 28. (β12) β 12
7. 4 β 10 29. (β26) β 26
8. 4 β 20 30. (β13) β 21
9. 4 β 80 31. (β25) β 75
10. 4 β 100 32. (β411) β 811
11. 4 β (β1) 33. (β234) β 543
12. 4 β (β2) 34. (β3) β (β1)
13. 4 β (β3) 35. (β3) β (β2)
14. 4 β (β7) 36. (β3) β (β3)
15. 4 β (β17) 37. (β3) β (β4)
16. 4 β (β27) 38. (β3) β (β8)
17. 4 β (β127) 39. (β30) β (β45)
18. 14 β (β6) 40. (β27) β (β13)
19. 23 β (β8) 41. (β13) β (β27)
20. 8 β (β23) 42. (β4) β (β3)
21. 51 β (β3) 43. (β3) β (β4)
22. 48 β (β5) 44. (β1,066) β (β34)
Number Correct: ______
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Integer SubtractionβRound 1 [KEY]
Directions: Determine the difference of the integers, and write it in the column to the right.
1. 4 β 2 π 23. (β6) β 5 βππ
2. 4 β 3 π 24. (β6) β 7 βππ
3. 4 β 4 π 25. (β6) β 9 βππ
4. 4 β 5 βπ 26. (β14) β 9 βππ
5. 4 β 6 βπ 27. (β25) β 9 βππ
6. 4 β 9 βπ 28. (β12) β 12 βππ
7. 4 β 10 βπ 29. (β26) β 26 βππ
8. 4 β 20 βππ 30. (β13) β 21 βππ
9. 4 β 80 βππ 31. (β25) β 75 βπππ
10. 4 β 100 βππ 32. (β411) β 811 βπ, πππ
11. 4 β (β1) π 33. (β234) β 543 βπππ
12. 4 β (β2) π 34. (β3) β (β1) βπ
13. 4 β (β3) π 35. (β3) β (β2) βπ
14. 4 β (β7) ππ 36. (β3) β (β3) π
15. 4 β (β17) ππ 37. (β3) β (β4) π
16. 4 β (β27) ππ 38. (β3) β (β8) π
17. 4 β (β127) πππ 39. (β30) β (β45) ππ
18. 14 β (β6) ππ 40. (β27) β (β13) βππ
19. 23 β (β8) ππ 41. (β13) β (β27) ππ
20. 8 β (β23) ππ 42. (β4) β (β3) βπ
21. 51 β (β3) ππ 43. (β3) β (β4) π
22. 48 β (β5) ππ 44. (β1,066) β (β34) βπ, πππ
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Integer SubtractionβRound 2
Directions: Determine the difference of the integers, and write it in the column to the right.
1. 3 β 2 23. (β8) β 5
2. 3 β 3 24. (β8) β 7
3. 3 β 4 25. (β8) β 9
4. 3 β 5 26. (β15) β 9
5. 3 β 6 27. (β35) β 9
6. 3 β 9 28. (β22) β 22
7. 3 β 10 29. (β27) β 27
8. 3 β 20 30. (β14) β 21
9. 3 β 80 31. (β22) β 72
10. 3 β 100 32. (β311) β 611
11. 3 β (β1) 33. (β345) β 654
12. 3 β (β2) 34. (β2) β (β1)
13. 3 β (β3) 35. (β2) β (β2)
14. 3 β (β7) 36. (β2) β (β3)
15. 3 β (β17) 37. (β2) β (β4)
16. 3 β (β27) 38. (β2) β (β8)
17. 3 β (β127) 39. (β20) β (β45)
18. 13 β (β6) 40. (β24) β (β13)
19. 24 β (β8) 41. (β13) β (β24)
20. 5 β (β23) 42. (β5) β (β3)
21. 61 β (β3) 43. (β3) β (β5)
22. 58 β (β5) 44. (β1,034) β (β31)
Number Correct: ______
Improvement: ______
6β8 Xβ’X
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Integer SubtractionβRound 2 [KEY]
Directions: Determine the difference of the integers, and write it in the column to the right.
1. 3 β 2 π 23. (β8) β 5 βππ
2. 3 β 3 π 24. (β8) β 7 βππ
3. 3 β 4 βπ 25. (β8) β 9 βππ
4. 3 β 5 βπ 26. (β15) β 9 βππ
5. 3 β 6 βπ 27. (β35) β 9 βππ
6. 3 β 9 βπ 28. (β22) β 22 βππ
7. 3 β 10 βπ 29. (β27) β 27 βππ
8. 3 β 20 βππ 30. (β14) β 21 βππ
9. 3 β 80 βππ 31. (β22) β 72 βππ
10. 3 β 100 βππ 32. (β311) β 611 βπππ
11. 3 β (β1) π 33. (β345) β 654 βπππ
12. 3 β (β2) π 34. (β2) β (β1) βπ
13. 3 β (β3) π 35. (β2) β (β2) π
14. 3 β (β7) ππ 36. (β2) β (β3) π
15. 3 β (β17) ππ 37. (β2) β (β4) π
16. 3 β (β27) ππ 38. (β2) β (β8) π
17. 3 β (β127) πππ 39. (β20) β (β45) ππ
18. 13 β (β6) ππ 40. (β24) β (β13) βππ
19. 24 β (β8) ππ 41. (β13) β (β24) ππ
20. 5 β (β23) ππ 42. (β5) β (β3) βπ
21. 61 β (β3) ππ 43. (β3) β (β5) π
22. 58 β (β5) ππ 44. (β1,034) β (β31) βπ, πππ
6β8 Xβ’X
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Integer MultiplicationβRound 1
Directions: Determine the product of the integers, and write it in the column to the right.
1. β2 β β 8 23. β14 β β 12
2. β4 β 3 24. 15 β β 13
3. 5 β β 7 25. 16 β β 18
4. 1 β β 1 26. 24 β β 17
5. β6 β 9 27. β32 β β 21
6. β2 β β 7 28. 19 β β 27
7. 8 β β 3 29. β39 β 10
8. 0 ββ 9 30. 43 β 22
9. 12 β β 5 31. 11 β β 33
10. β4 β 2 32. β29 β β 45
11. β1 β β 6 33. 37 β β 44
12. 10 β β 4 34. β87 β β 100
13. 14 β β 3 35. 92 β β 232
14. β5 β β 13 36. 456 β 87
15. β16 β β 8 37. β143 β 76
16. 18 β β 2 38. 439 β β 871
17. β15 β 7 39. β286 ββ 412
18. β19 β 1 40. β971 β 342
19. 12 β 12 41. β773 ββ 407
20. 9 β β 17 42. β820 β 638
21. β8 β β 14 43. 591 β β 734
22. β7 β 13 44. 491 β β 197
Number Correct: ______
6β8 Xβ’X
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Integer MultiplicationβRound 1 [KEY]
Directions: Determine the product of the integers, and write it in the column to the right.
1. β2 β β 8 ππ 23. β14 β β 12 πππ
2. β4 β 3 βππ 24. 15 β β 13 βπππ
3. 5 β β 7 βππ 25. 16 β β 18 βπππ
4. 1 β β 1 βπ 26. 24 β β 17 βπππ
5. β6 β 9 βππ 27. β32 β β 21 πππ
6. β2 β β 7 ππ 28. 19 β β 27 βπππ
7. 8 β β 3 βππ 29. β39 β 10 βπππ
8. 0 ββ 9 π 30. 43 β 22 πππ
9. 12 β β 5 βππ 31. 11 β β 33 βπππ
10. β4 β 2 βπ 32. β29 β β 45 π, πππ
11. β1 β β 6 π 33. 37 β β 44 βπ, πππ
12. 10 β β 4 βππ 34. β87 β β 100 π, πππ
13. 14 β β 3 βππ 35. 92 β β 232 βππ, πππ
14. β5 β β 13 ππ 36. 456 β 87 ππ, πππ
15. β16 β β 8 πππ 37. β143 β 76 βππ, πππ
16. 18 β β 2 βππ 38. 439 β β 871 βπππ, πππ
17. β15 β 7 βπππ 39. β286 ββ 412 πππ, πππ
18. β19 β 1 βππ 40. β971 β 342 βπππ, πππ
19. 12 β 12 πππ 41. β773 ββ 407 πππ, πππ
20. 9 β β 17 βπππ 42. β820 β 638 βπππ, πππ
21. β8 β β 14 πππ 43. 591 β β 734 βπππ, πππ
22. β7 β 13 βππ 44. 491 β β 197 βππ, πππ
6β8 Xβ’X
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Integer MultiplicationβRound 2
Directions: Determine the product of the integers, and write it in the column to the right.
1. β9 β β 7 23. β22 β 14
2. 0 β β 4 24. β18 β β 32
3. 3 β β 5 25. β24 β 19
4. 6 β β 8 26. 47 β 21
5. β2 β 1 27. 17 β β 39
6. β6 β 5 28. β16 β β 28
7. β10 β β 12 29. β67 β β 81
8. 11 β β 4 30. β36 β 44
9. 3 β 8 31. β50 β 23
10. 12 β β 7 32. 66 β β 71
11. β1 β 8 33. 82 β β 29
12. 5 β β 10 34. β32 β 231
13. 3 β β 13 35. 89 β β 744
14. 15 β β 8 36. 623 β β 22
15. β9 β 14 37. β870 ββ 46
16. β17 β 5 38. 179 β 329
17. 16 β 2 39. β956 β 723
18. 19 β β 7 40. 874 β β 333
19. β6 β 13 41. 908 β β 471
20. 1 β β 18 42. β661 ββ 403
21. β14 β β 3 43. β520 ββ 614
22. β10 β β 17 44. β309 β 911
Number Correct: ______
Improvement: ______
6β8 Xβ’X
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Integer MultiplicationβRound 2 [KEY]
Directions: Determine the product of the integers, and write it in the column to the right.
1. β9 β β 7 ππ 23. β22 β 14 βπππ
2. 0 β β 4 π 24. β18 β β 32 πππ
3. 3 β β 5 βππ 25. β24 β 19 βπππ
4. 6 β β 8 βππ 26. 47 β 21 πππ
5. β2 β 1 βπ 27. 17 β β 39 βπππ
6. β6 β 5 βππ 28. β16 β β 28 πππ
7. β10 β β 12 πππ 29. β67 β β 81 π, πππ
8. 11 β β 4 βππ 30. β36 β 44 βπ, πππ
9. 3 β 8 ππ 31. β50 β 23 βπ, πππ
10. 12 β β 7 βππ 32. 66 β β 71 βπ, πππ
11. β1 β 8 βπ 33. 82 β β 29 βπ, πππ
12. 5 β β 10 βππ 34. β32 β 231 βπ, πππ
13. 3 β β 13 βππ 35. 89 β β 744 ππ, πππ
14. 15 β β 8 βπππ 36. 623 β β 22 βππ, πππ
15. β9 β 14 βπππ 37. β870 ββ 46 ππ, πππ
16. β17 β 5 βππ 38. 179 β 329 ππ, πππ
17. 16 β 2 ππ 39. β956 β 723 βπππ, πππ
18. 19 β β 7 βπππ 40. 874 β β 333 βπππ, πππ
19. β6 β 13 βππ 41. 908 β β 471 βπππ, πππ
20. 1 β β 18 βππ 42. β661 ββ 403 πππ, πππ
21. β14 β β 3 ππ 43. β520 ββ 614 πππ, πππ
22. β10 β β 17 πππ 44. β309 β 911 βπππ, πππ
6β8 Xβ’X
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Integer DivisionβRound 1
Directions: Determine the quotient of the integers, and write it in the column to the right.
1. 4 Γ· 1 23. β16 Γ· (β4)
2. 4 Γ· (β1) 24. 16 Γ· (β2)
3. β4 Γ· (β1) 25. β16 Γ· 4
4. β4 Γ· 1 26. β20 Γ· 4
5. 6 Γ· 2 27. β20 Γ· (β4)
6. β6 Γ· (β2) 28. β28 Γ· 4
7. β6 Γ· 2 29. 28 Γ· (β7)
8. 6 Γ· β2 30. β28 Γ· (β7)
9. 8 Γ· (β4) 31. β40 Γ· (β5)
10. β8 Γ· (β4) 32. 56 Γ· (β7)
11. β8 Γ· 4 33. 96 Γ· (β3)
12. 8 Γ· 4 34. β121 Γ· (β11)
13. 9 Γ· (β3) 35. 169 Γ· (β13)
14. β9 Γ· 3 36. β175 Γ· 25
15. β10 Γ· 5 37. 1 Γ· 4
16. 10 Γ· (β2) 38. β1 Γ· 4
17. β10 Γ· (β2) 39. β1 Γ· (β4)
18. β10 Γ· (β5) 40. β3 Γ· (β4)
19. β14 Γ· 7 41. β5 Γ· 20
20. 14 Γ· (β2) 42. 6 Γ· (β18)
21. β14 Γ· (β2) 43. β24 Γ· 48
22. β14 Γ· (β7) 44. β16 Γ· 64
Number Correct: ______
6β8 Xβ’X
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Integer DivisionβRound 1 [KEY]
Directions: Determine the quotient of the integers, and write it in the column to the right.
1. 4 Γ· 1 π 23. β16 Γ· (β4) π
2. 4 Γ· (β1) βπ 24. 16 Γ· (β2) βπ
3. β4 Γ· (β1) π 25. β16 Γ· 4 βπ
4. β4 Γ· 1 βπ 26. β20 Γ· 4 βπ
5. 6 Γ· 2 π 27. β20 Γ· (β4) π
6. β6 Γ· (β2) π 28. β28 Γ· 4 βπ
7. β6 Γ· 2 βπ 29. 28 Γ· (β7) βπ
8. 6 Γ· β2 βπ 30. β28 Γ· (β7) π
9. 8 Γ· (β4) βπ 31. β40 Γ· (β5) π
10. β8 Γ· (β4) π 32. 56 Γ· (β7) βπ
11. β8 Γ· 4 βπ 33. 96 Γ· (β3) βππ
12. 8 Γ· 4 π 34. β121 Γ· (β11) ππ
13. 9 Γ· (β3) βπ 35. 169 Γ· (β13) βππ
14. β9 Γ· 3 βπ 36. β175 Γ· 25 βπ
15. β10 Γ· 5 βπ 37. 1 Γ· 4 π
π
16. 10 Γ· (β2) βπ 38. β1 Γ· 4 βπ
π
17. β10 Γ· (β2) π 39. β1 Γ· (β4) π
π
18. β10 Γ· (β5) π 40. β3 Γ· (β4) π
π
19. β14 Γ· 7 βπ 41. β5 Γ· 20 βπ
ππor β
π
π
20. 14 Γ· (β2) βπ 42. 6 Γ· (β18) βπ
ππor β
π
π
21. β14 Γ· (β2) π 43. β24 Γ· 48 βπ
22. β14 Γ· (β7) π 44. β16 Γ· 64 βππ
ππor β
π
π
6β8 Xβ’X
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Integer DivisionβRound 2
Directions: Determine the quotient of the integers, and write it in the column to the right.
1. 5 Γ· 1 23. β18 Γ· (β9)
2. 5 Γ· (β1) 24. 18 Γ· (β2)
3. β5 Γ· (β1) 25. β18 Γ· 9
4. β5 Γ· 1 26. β24 Γ· 4
5. 6 Γ· 3 27. β24 Γ· (β4)
6. β6 Γ· (β3) 28. β24 Γ· 6
7. β6 Γ· 3 29. 30 Γ· (β6)
8. 6 Γ· β3 30. β30 Γ· (β5)
9. 8 Γ· (β2) 31. β48 Γ· (β6)
10. β8 Γ· (β2) 32. 64 Γ· (β4)
11. β8 Γ· 2 33. 105 Γ· (β7)
12. 8 Γ· 2 34. β144 Γ· (β12)
13. β9 Γ· (β3) 35. 196 Γ· (β14)
14. 9 Γ· 3 36. β225 Γ· 25
15. β12 Γ· 6 37. 2 Γ· 4
16. 12 Γ· (β2) 38. β2 Γ· 4
17. β12 Γ· (β2) 39. β2 Γ· (β4)
18. β12 Γ· (β6) 40. β4 Γ· (β8)
19. β16 Γ· 8 41. β5 Γ· 40
20. 16 Γ· (β2) 42. 6 Γ· (β42)
21. β16 Γ· (β2) 43. β25 Γ· 75
22. β16 Γ· (β8) 44. β18 Γ· 108
Number Correct: ______
Improvement: ______
6β8 Xβ’X
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Integer DivisionβRound 2 [KEY]
Directions: Determine the quotient of the integers, and write it in the column to the right.
1. 5 Γ· 1 π 23. β18 Γ· (β9) π
2. 5 Γ· (β1) βπ 24. 18 Γ· (β2) βπ
3. β5 Γ· (β1) π 25. β18 Γ· 9 βπ
4. β5 Γ· 1 βπ 26. β24 Γ· 4 βπ
5. 6 Γ· 3 π 27. β24 Γ· (β4) π
6. β6 Γ· (β3) π 28. β24 Γ· 6 βπ
7. β6 Γ· 3 βπ 29. 30 Γ· (β6) βπ
8. 6 Γ· β3 βπ 30. β30 Γ· (β5) π
9. 8 Γ· (β2) βπ 31. β48 Γ· (β6) π
10. β8 Γ· (β2) π 32. 64 Γ· (β4) βππ
11. β8 Γ· 2 βπ 33. 105 Γ· (β7) βππ
12. 8 Γ· 2 π 34. β144 Γ· (β12) ππ
13. β9 Γ· (β3) π 35. 196 Γ· (β14) βππ
14. 9 Γ· 3 π 36. β225 Γ· 25 βπ
15. β12 Γ· 6 βπ 37. 2 Γ· 4 π
πor
π
π
16. 12 Γ· (β2) βπ 38. β2 Γ· 4 βπ
πor β
π
π
17. β12 Γ· (β2) π 39. β2 Γ· (β4) π
πor
π
π
18. β12 Γ· (β6) π 40. β4 Γ· (β8) π
πor
π
π
19. β16 Γ· 8 βπ 41. β5 Γ· 40 βπ
ππor β
π
π
20. 16 Γ· (β2) βπ 42. 6 Γ· (β42) βπ
ππor β
π
π
21. β16 Γ· (β2) π 43. β25 Γ· 75 βππ
ππor β
π
π
22. β16 Γ· (β8) π 44. β18 Γ· 108 βππ
πππor β
π
π
6β8 Xβ’X
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Generating Equivalent ExpressionsβRound 1
Directions: Write each as an equivalent expression in standard form as quickly and accurately as possible within the
allotted time.
1. 1 + 1 23. 4π₯ + 6π₯ β 12π₯
2. 1 + 1 + 1 24. 4π₯ β 6π₯ + 4π₯
3. (1 + 1) + 1 25. 7π₯ β 2π₯ + 3
4. (1 + 1) + (1 + 1) 26. (4π₯ + 3) + π₯
5. (1 + 1) + (1 + 1 + 1) 27. (4π₯ + 3) + 2π₯
6. π₯ + π₯ 28. (4π₯ + 3) + 3π₯
7. π₯ + π₯ + π₯ 29. (4π₯ + 3) + 5π₯
8. (π₯ + π₯) + π₯ 30. (4π₯ + 3) + 6π₯
9. (π₯ + π₯) + (π₯ + π₯) 31. (11π₯ + 2) β 2
10. (π₯ + π₯) + (π₯ + π₯ + π₯) 32. (11π₯ + 2) β 3
11. (π₯ + π₯ + π₯) + (π₯ + π₯ + π₯) 33. (11π₯ + 2) β 4
12. 2π₯ + π₯ 34. (11π₯ + 2) β 7
13. 3π₯ + π₯ 35. (3π₯ β 9) + (3π₯ + 5)
14. 4π₯ + π₯ 36. (11 β 5π₯) + (4π₯ + 2)
15. 7π₯ + π₯ 37. (2π₯ + 3π¦) + (4π₯ + π¦)
16. 7π₯ + 2π₯ 38. (5π₯ + 1.3π¦) + (2.9π₯ β 0.6π¦)
17. 7π₯ + 3π₯ 39. (2.6π₯ β 4.8π¦) + (6.5π₯ β 1.1π¦)
18. 10π₯ β π₯ 40. (3
4π₯ β
1
2π¦) + (β
7
4π₯ β
5
2π¦)
19. 10π₯ β 5π₯ 41. (β2
5π₯ β
7
9π¦) + (β
7
10π₯ β
2
3π¦)
20. 10π₯ β 10π₯ 42. (1
2π₯ β
1
4π¦) + (β
3
5π₯ +
5
6π₯)
21. 10π₯ β 11π₯ 43. (1.2π₯ β3
4π¦) β (β
3
5π₯ + 2.25π₯)
22. 10π₯ β 12π₯ 44. (3.375π₯ β 8.9π¦) β (β75
8π₯ β 5
2
5π¦)
Number Correct: ______
6β8 Xβ’X
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Fluency Support for Grades 6β8 Date: 4/2/15
90
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Generating Equivalent ExpressionsβRound 1 [KEY]
Directions: Write each as an equivalent expression in standard form as quickly and accurately as possible within the
allotted time.
1. 1 + 1 π 23. 4π₯ + 6π₯ β 12π₯ βππ
2. 1 + 1 + 1 π 24. 4π₯ β 6π₯ + 4π₯ ππ
3. (1 + 1) + 1 π 25. 7π₯ β 2π₯ + 3 ππ + π
4. (1 + 1) + (1 + 1) π 26. (4π₯ + 3) + π₯ ππ + π
5. (1 + 1) + (1 + 1 + 1) π 27. (4π₯ + 3) + 2π₯ ππ + π
6. π₯ + π₯ ππ 28. (4π₯ + 3) + 3π₯ ππ + π
7. π₯ + π₯ + π₯ ππ 29. (4π₯ + 3) + 5π₯ ππ + π
8. (π₯ + π₯) + π₯ ππ 30. (4π₯ + 3) + 6π₯ πππ + π
9. (π₯ + π₯) + (π₯ + π₯) ππ 31. (11π₯ + 2) β 2 πππ
10. (π₯ + π₯) + (π₯ + π₯ + π₯) ππ 32. (11π₯ + 2) β 3 πππ β π
11. (π₯ + π₯ + π₯) + (π₯ + π₯
+ π₯) ππ 33. (11π₯ + 2) β 4 πππ β π
12. 2π₯ + π₯ ππ 34. (11π₯ + 2) β 7 πππ β π
13. 3π₯ + π₯ ππ 35. (3π₯ β 9) + (3π₯ + 5) ππ β π
14. 4π₯ + π₯ ππ 36. (11 β 5π₯) + (4π₯ + 2) ππ β π
or β π + ππ
15. 7π₯ + π₯ ππ 37. (2π₯ + 3π¦) + (4π₯ + π¦) ππ + ππ
16. 7π₯ + 2π₯ ππ 38. (5π₯ + 1.3π¦) + (2.9π₯ β 0.6π¦) π. ππ + π. ππ
17. 7π₯ + 3π₯ πππ 39. (2.6π₯ β 4.8π¦) + (6.5π₯ β 1.1π¦) π. ππ β π. ππ
18. 10π₯ β π₯ ππ 40. (3
4π₯ β
1
2π¦) + (β
7
4π₯ β
5
2π¦) βπ β ππ
19. 10π₯ β 5π₯ ππ 41. (β2
5π₯ β
7
9π¦) + (β
7
10π₯ β
2
3π¦) β
ππ
πππ β
ππ
ππ
20. 10π₯ β 10π₯ π 42. (1
2π₯ β
1
4π¦) + (β
3
5π₯ +
5
6π₯) β
π
πππ +
π
πππ
21. 10π₯ β 11π₯ βππ or β π 43. (1.2π₯ β3
4π¦) β (β
3
5π₯ + 2.25π₯) π
π
ππ + π
π
ππ
22. 10π₯ β 12π₯ βππ 44. (3.375π₯ β 8.9π¦) β (β75
8π₯ β 5
2
5π¦) πππ β
π
ππ
6β8 Xβ’X
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Generating Equivalent ExpressionsβRound 2
Directions: Write each as an equivalent expression in standard form as quickly and accurately as possible within the
allotted time.
1. 1 + 1 + 1 23. 3π₯ + 5π₯ β 4π₯
2. 1 + 1 + 1 + 1 24. 8π₯ β 6π₯ + 4π₯
3. (1 + 1 + 1) + 1 25. 7π₯ β 4π₯ + 5
4. (1 + 1 + 1) + (1 + 1) 26. (9π₯ β 1) + π₯
5. (1 + 1 + 1) + (1 + 1 + 1) 27. (9π₯ β 1) + 2π₯
6. π₯ + π₯ + π₯ 28. (9π₯ β 1) + 3π₯
7. π₯ + π₯ + π₯ + π₯ 29. (9π₯ β 1) + 5π₯
8. (π₯ + π₯ + π₯) + π₯ 30. (9π₯ β 1) + 6π₯
9. (π₯ + π₯ + π₯) + (π₯ + π₯) 31. (β3π₯ + 3) β 2
10. (π₯ + π₯ + π₯) + (π₯ + π₯ + π₯) 32. (β3π₯ + 3) β 3
11. (π₯ + π₯ + π₯ + π₯) + (π₯ + π₯) 33. (β3π₯ + 3) β 4
12. π₯ + 2π₯ 34. (β3π₯ + 3) β 5
13. π₯ + 4π₯ 35. (5π₯ β 2) + (2π₯ + 5)
14. π₯ + 6π₯ 36. (8 β π₯) + (3π₯ + 2)
15. π₯ + 8π₯ 37. (5π₯ + π¦) + (π₯ + π¦)
16. 7π₯ + π₯ 38. (5
2π₯ +
3
2π¦) + (
11
2π₯ β
3
4π¦)
17. 8π₯ + 2π₯ 39. (1
6π₯ β
3
8π¦) + (
2
3π₯ β
7
4π¦)
18. 2π₯ β π₯ 40. (9.7π₯ β 3.8π¦) + (β2.8π₯ + 4.5π¦)
19. 2π₯ β 2π₯ 41. (1.65π₯ β 2.73π¦) + (β1.35π₯ + 3.76π¦)
20. 2π₯ β 3π₯ 42. (6.51π₯ β 4.39π¦) + (β7.46π₯ + 8.11π₯)
21. 2π₯ β 4π₯ 43. (0.7π₯ β2
9π¦) β (β
7
5π₯ + 2
1
3π₯)
22. 2π₯ β 8π₯ 44. (8.4π₯ β 2.25π¦) β (β21
2π₯ β 4
3
8π¦)
Number Correct: ______
Improvement: ______
6β8 Xβ’X
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Fluency Support for Grades 6β8 Date: 4/2/15
92
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Generating Equivalent ExpressionsβRound 2 [KEY]
Directions: Write each as an equivalent expression in standard form as quickly and accurately as possible within the
allotted time.
1. 1 + 1 + 1 π 23. 3π₯ + 5π₯ β 4π₯ ππ
2. 1 + 1 + 1 + 1 π 24. 8π₯ β 6π₯ + 4π₯ ππ
3. (1 + 1 + 1) + 1 π 25. 7π₯ β 4π₯ + 5 ππ + π
4. (1 + 1 + 1) + (1 + 1) π 26. (9π₯ β 1) + π₯ πππ β π
5. (1 + 1 + 1) + (1 + 1 + 1) π 27. (9π₯ β 1) + 2π₯ πππ β π
6. π₯ + π₯ + π₯ ππ 28. (9π₯ β 1) + 3π₯ πππ β π
7. π₯ + π₯ + π₯ + π₯ ππ 29. (9π₯ β 1) + 5π₯ πππ β π
8. (π₯ + π₯ + π₯) + π₯ ππ 30. (9π₯ β 1) + 6π₯ πππ β π
9. (π₯ + π₯ + π₯) + (π₯ + π₯) ππ 31. (β3π₯ + 3) β 2 βππ + π
10. (π₯ + π₯ + π₯) + (π₯ + π₯ + π₯) ππ 32. (β3π₯ + 3) β 3 βππ
11. (π₯ + π₯ + π₯ + π₯) + (π₯ + π₯) ππ 33. (β3π₯ + 3) β 4 βππ β π
12. π₯ + 2π₯ ππ 34. (β3π₯ + 3) β 5 βππ β π
13. π₯ + 4π₯ ππ 35. (5π₯ β 2) + (2π₯ + 5) ππ + π
14. π₯ + 6π₯ ππ 36. (8 β π₯) + (3π₯ + 2) ππ + ππ
15. π₯ + 8π₯ ππ 37. (5π₯ + π¦) + (π₯ + π¦) ππ + ππ
16. 7π₯ + π₯ ππ 38. (5
2π₯ +
3
2π¦) + (
11
2π₯ β
3
4π¦) ππ +
π
ππ
17. 8π₯ + 2π₯ πππ 39. (1
6π₯ β
3
8π¦) + (
2
3π₯ β
7
4π¦)
π
ππ β
ππ
ππ
18. 2π₯ β π₯ π or ππ 40. (9.7π₯ β 3.8π¦) + (β2.8π₯ + 4.5π¦) π. ππ + π. ππ
19. 2π₯ β 2π₯ π 41. (1.65π₯ β 2.73π¦) + (β1.35π₯ + 3.76π¦) π. ππ + π. πππ
20. 2π₯ β 3π₯ βπ or β ππ 42. (6.51π₯ β 4.39π¦) + (β7.46π₯ + 8.11π₯) βπ. πππ + π. πππ
21. 2π₯ β 4π₯ βππ 43. (0.7π₯ β2
9π¦) β (β
7
5π₯ + 2
1
3π₯) β
ππ
πππ β π
π
ππ
22. 2π₯ β 8π₯ βππ 44. (8.4π₯ β 2.25π¦) β (β21
2π₯ β 4
3
8π¦) ππ
π
πππ + π
π
ππ
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Equations
Progression of Exercises
Determine the value of the variable.
Set 1
1. π₯ + 1 = 5
π = π
2. π₯ + 3 = 5
π = π
3. π₯ + 6 = 5
π = βπ
4. π₯ β 5 = 2
π = π
5. π₯ β 5 = 8
π = ππ
Set 2
1. 3π₯ = 15
π = π
2. 3π₯ = 0
π = π
3. 3π₯ = β3
π = βπ
4. β9π₯ = 18
π = βπ
5. βπ₯ = 18
π = βππ
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Set 3
1. 1
7π₯ = 5
π = ππ
2. 2
7π₯ = 10
π = ππ
3. 3
7π₯ = 15
π = ππ
4. 4
7π₯ = 20
π = ππ
5. β5
7π₯ = β25
π = ππ
Set 4
1. 2π₯ + 4 = 12
π = π
2. 2π₯ β 5 = 13
π = π
3. 2π₯ + 6 = 14
π = π
4. 3π₯ β 6 = 18
π = π
5. β4π₯ + 6 = 22
π = βπ
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Set 5
1. 2π₯ + 0.5 = 6.5
π = π
2. 3π₯ β 0.5 = 8.5
π = π
3. 5π₯ + 3 = 8.5
π = π. π
4. 5π₯ β 4 = 1.5
π = π. π
5. β7π₯ + 1.5 = 5
π = βπ. π
Set 6
1. 2(π₯ + 3) = 4
π = βπ
2. 5(π₯ + 3) = 10
π = βπ
3. 5(π₯ β 3) = 10
π = π
4. β2(π₯ β 3) = 8
π = βπ
5. β3(π₯ + 4) = 3
π = βπ
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Inequalities
Progression of Exercises
Set 1
1. π₯ + 1 > 8
π > π
2. π₯ + 3 > 8
π > π
3. π₯ + 10 > 8
π > βπ
4. π₯ β 2 > 3
π > π
5. π₯ β 4 > 3
π > π
Set 2
1. 3π₯ β€ 15
π β€ π
2. 3π₯ β€ 21
π β€ π
3. βπ₯ β€ 4
π β₯ βπ
4. β2π₯ β€ 4
π β₯ βπ
5. βπ₯ β€ β4
π β₯ π
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Set 3
1. 1
2π₯ < 1
π < π
2. 1
2π₯ < 3
π < π
3. β1
5π₯ < 2
π > βππ
4. β2
5π₯ < 2
π > βπ
5. β3
5π₯ < 3
π > βπ
Set 4
1. 2π₯ + 4 β₯ 8
π β₯ π
2. 2π₯ β 3 β₯ 5
π β₯ π
3. β2π₯ + 1 β₯ 7
π β€ βπ
4. β3π₯ + 1 β₯ β8
π β€ π
5. β3π₯ β 5 β₯ 10
π β€ βπ
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Set 5
1. 2π₯ β 0.5 > 5.5
π > π
2. 3π₯ + 1.5 > 4.5
π > π
3. 5π₯ β 3 > 4.5
π > π. π
4. β5π₯ + 2 > 8.5
π < βπ. π
5. β9π₯ β 3.5 > 1
π < βπ. π
Set 6
1. 2(π₯ + 3) β€ 4
π β€ βπ
2. 3(π₯ + 3) β€ 6
π β€ βπ
3. 4(π₯ + 3) β€ 8
π β€ βπ
4. β5(π₯ β 3) β€ β10
π β₯ π
5. β2(π₯ + 3) β€ 8
π β₯ βπ
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Fractions, Decimals, and PercentsβRound 1
Directions: Write each number in the alternate form indicated.
1. 20
100 as a percent 23.
9
10 as a percent
2. 40
100 as a percent 24.
9
20 as a percent
3. 80
100 as a percent 25.
9
25 as a percent
4. 85
100 as a percent 26.
9
50 as a percent
5. 95
100 as a percent 27.
9
75 as a percent
6. 100
100 as a percent 28.
18
75 as a percent
7. 10
10 as a percent 29.
36
75 as a percent
8. 1
1 as a percent 30. 96% as a fraction
9. 1
10 as a percent 31. 92% as a fraction
10. 2
10 as a percent 32. 88% as a fraction
11. 4
10 as a percent 33. 44% as a fraction
12. 75% as a decimal 34. 22% as a fraction
13. 25% as a decimal 35. 3% as a decimal
14. 15% as a decimal 36. 30% as a decimal
15. 10% as a decimal 37. 33% as a decimal
16. 5% as a decimal 38. 33.3% as a decimal
17. 30% as a fraction 39. 3.3% as a decimal
18. 60% as a fraction 40. 0.3% as a decimal
19. 90% as a fraction 41. 1
3 as a percent
20. 50% as a fraction 42. 1
9 as a percent
21. 25% as a fraction 43. 2
9 as a percent
22. 20% as a fraction 44. 8
9 as a percent
Number Correct: ______
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Fractions, Decimals, and PercentsβRound 1 [KEY]
Directions: Write each number in the alternate form indicated.
1. 20
100 as a percent ππ% 23.
9
10 as a percent ππ%
2. 40
100 as a percent ππ% 24.
9
20 as a percent ππ%
3. 80
100 as a percent ππ% 25.
9
25 as a percent ππ%
4. 85
100 as a percent ππ% 26.
9
50 as a percent ππ%
5. 95
100 as a percent ππ% 27.
9
75 as a percent ππ%
6. 100
100 as a percent πππ% 28.
18
75 as a percent ππ%
7. 10
10 as a percent πππ% 29.
36
75 as a percent ππ%
8. 1
1 as a percent πππ% 30. 96% as a fraction
ππ
ππ or
ππ
ππ
9. 1
10 as a percent ππ% 31. 92% as a fraction
ππ
ππ
10. 2
10 as a percent ππ% 32. 88% as a fraction
ππ
ππ
11. 4
10 as a percent ππ% 33. 44% as a fraction
ππ
ππ
12. 75% as a decimal π. ππ 34. 22% as a fraction ππ
ππ
13. 25% as a decimal π. ππ 35. 3% as a decimal π. ππ
14. 15% as a decimal π. ππ 36. 30% as a decimal π. π
15. 10% as a decimal π. π 37. 33% as a decimal π. ππ
16. 5% as a decimal π. ππ 38. 33.3% as a decimal π. πππ
17. 30% as a fraction π
ππ 39. 3.3% as a decimal π. πππ
18. 60% as a fraction π
π 40. 0.3% as a decimal π. πππ
19. 90% as a fraction π
ππ 41.
1
3 as a percent ππ
π
π%
20. 50% as a fraction π
π 42.
1
9 as a percent ππ
π
π%
21. 25% as a fraction π
π 43.
2
9 as a percent ππ
π
π%
22. 20% as a fraction π
π 44.
8
9 as a percent ππ
π
π%
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Fractions, Decimals, and PercentsβRound 2
Directions: Write each number in the alternate form indicated.
1. 30
100 as a percent 23.
6
10 as a percent
2. 60
100 as a percent 24.
6
20 as a percent
3. 70
100 as a percent 25.
6
25 as a percent
4. 75
100 as a percent 26.
6
50 as a percent
5. 90
100 as a percent 27.
6
75 as a percent
6. 50
100 as a percent 28.
12
75 as a percent
7. 5
10 as a percent 29.
24
75 as a percent
8. 1
2 as a percent 30. 64% as a fraction
9. 1
4 as a percent 31. 60% as a fraction
10. 1
8 as a percent 32. 56% as a fraction
11. 3
8 as a percent 33. 28% as a fraction
12. 60% as a decimal 34. 14% as a fraction
13. 45% as a decimal 35. 9% as a decimal
14. 30% as a decimal 36. 90% as a decimal
15. 6% as a decimal 37. 99% as a decimal
16. 3% as a decimal 38. 99.9% as a decimal
17. 3% as a fraction 39. 9.9% as a decimal
18. 6% as a fraction 40. 0.9% as a decimal
19. 60% as a fraction 41. 4
9 as a percent
20. 30% as a fraction 42. 5
9 as a percent
21. 45% as a fraction 43. 2
3 as a percent
22. 15% as a fraction 44. 1
6 as a percent
Number Correct: ______
Improvement: ______
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Fractions, Decimals, and PercentsβRound 2 [KEY]
Directions: Write each number in the alternate form indicated.
1. 30
100 as a percent ππ% 23.
6
10 as a percent ππ%
2. 60
100 as a percent ππ% 24.
6
20 as a percent ππ%
3. 70
100 as a percent ππ% 25.
6
25 as a percent ππ%
4. 75
100 as a percent ππ% 26.
6
50 as a percent ππ%
5. 90
100 as a percent ππ% 27.
6
75 as a percent π%
6. 50
100 as a percent ππ% 28.
12
75 as a percent ππ%
7. 5
10 as a percent ππ% 29.
24
75 as a percent ππ%
8. 1
2 as a percent ππ% 30. 64% as a fraction
ππ
ππ or
ππ
ππ
9. 1
4 as a percent ππ% 31. 60% as a fraction
ππ
ππ or
π
π
10. 1
8 as a percent ππ. π% 32. 56% as a fraction
ππ
ππ
11. 3
8 as a percent ππ. π% 33. 28% as a fraction
π
ππ
12. 60% as a decimal π. π 34. 14% as a fraction π
ππ
13. 45% as a decimal π. ππ 35. 9% as a decimal π. ππ
14. 30% as a decimal π. π 36. 90% as a decimal π. π
15. 6% as a decimal π. ππ 37. 99% as a decimal π. ππ
16. 3% as a decimal π. ππ 38. 99.9% as a decimal π. πππ
17. 3% as a fraction π
πππ 39. 9.9% as a decimal π. πππ
18. 6% as a fraction π
ππ 40. 0.9% as a decimal π. πππ
19. 60% as a fraction π
π 41.
4
9 as a percent ππ
π
π%
20. 30% as a fraction π
ππ 42.
5
9 as a percent ππ
π
π%
21. 45% as a fraction π
ππ 43.
2
3 as a percent ππ
π
π%
22. 15% as a fraction π
ππ 44.
1
6 as a percent ππ
π
π%
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Part, Whole, or PercentβRound 1
Directions: Find each missing value.
1. 1% of 100 is? 23. 10% of 22 is?
2. 2% of 100 is? 24. 20% of 22 is?
3. 3% of 100 is? 25. 30% of 22 is?
4. 4% of 100 is? 26. 50% of 22 is?
5. 5% of 100 is? 27. 25% of 22 is?
6. 9% of 100 is? 28. 75% of 22 is?
7. 10% of 100 is? 29. 80% of 22 is?
8. 10% of 200 is? 30. 85% of 22 is?
9. 10% of 300 is? 31. 90% of 22 is?
10. 10% of 500 is? 32. 95% of 22 is?
11. 10% of 550 is? 33. 5% of 22 is?
12. 10% of 570 is? 34. 15% of 80 is?
13. 10% of 470 is? 35. 15% of 60 is?
14. 10% of 170 is? 36. 15% of 40 is?
15. 10% of 70 is? 37. 30% of 40 is?
16. 10% of 40 is? 38. 30% of 70 is?
17. 10% of 20 is? 39. 30% of 60 is?
18. 10% of 25 is? 40. 45% of 80 is?
19. 10% of 35 is? 41. 45% of 120 is?
20. 10% of 36 is? 42. 120% of 40 is?
21. 10% of 37 is? 43. 120% of 50 is?
22. 10% of 37.5 is? 44. 120% of 55 is?
Number Correct: ______
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Part, Whole, or PercentβRound 1 [KEY]
Directions: Find each missing value.
1. 1% of 100 is? π 23. 10% of 22 is? π. π
2. 2% of 100 is? π 24. 20% of 22 is? π. π
3. 3% of 100 is? π 25. 30% of 22 is? π. π
4. 4% of 100 is? π 26. 50% of 22 is? ππ
5. 5% of 100 is? π 27. 25% of 22 is? π. π
6. 9% of 100 is? π 28. 75% of 22 is? ππ. π
7. 10% of 100 is? ππ 29. 80% of 22 is? ππ. π
8. 10% of 200 is? ππ 30. 85% of 22 is? ππ. π
9. 10% of 300 is? ππ 31. 90% of 22 is? ππ. π
10. 10% of 500 is? ππ 32. 95% of 22 is? ππ. π
11. 10% of 550 is? ππ 33. 5% of 22 is? π. π
12. 10% of 570 is? ππ 34. 15% of 80 is? ππ
13. 10% of 470 is? ππ 35. 15% of 60 is? π
14. 10% of 170 is? ππ 36. 15% of 40 is? π
15. 10% of 70 is? π 37. 30% of 40 is? ππ
16. 10% of 40 is? π 38. 30% of 70 is? ππ
17. 10% of 20 is? π 39. 30% of 60 is? ππ
18. 10% of 25 is? π. π 40. 45% of 80 is? ππ
19. 10% of 35 is? π. π 41. 45% of 120 is? ππ
20. 10% of 36 is? π. π 42. 120% of 40 is? ππ
21. 10% of 37 is? π. π 43. 120% of 50 is? ππ
22. 10% of 37.5 is? π. ππ 44. 120% of 55 is? ππ
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Part, Whole, or PercentβRound 2
Directions: Find each missing value.
1. 20% of 100 is? 23. 10% of 4 is?
2. 21% of 100 is? 24. 20% of 4 is?
3. 22% of 100 is? 25. 30% of 4 is?
4. 23% of 100 is? 26. 50% of 4 is?
5. 25% of 100 is? 27. 25% of 4 is?
6. 25% of 200 is? 28. 75% of 4 is?
7. 25% of 300 is? 29. 80% of 4 is?
8. 25% of 400 is? 30. 85% of 4 is?
9. 25% of 4000 is? 31. 90% of 4 is?
10. 50% of 4000 is? 32. 95% of 4 is?
11. 10% of 4000 is? 33. 5% of 4 is?
12. 10% of 4700 is? 34. 15% of 40 is?
13. 10% of 4600 is? 35. 15% of 30 is?
14. 10% of 4630 is? 36. 15% of 20 is?
15. 10% of 463 is? 37. 30% of 20 is?
16. 10% of 46.3 is? 38. 30% of 50 is?
17. 10% of 18 is? 39. 30% of 90 is?
18. 10% of 24 is? 40. 45% of 90 is?
19. 10% of 3.63 is? 41. 90% of 120 is?
20. 10% of 0.336 is? 42. 125% of 40 is?
21. 10% of 37 is? 43. 125% of 50 is?
22. 10% of 37.5 is? 44. 120% of 60 is?
Number Correct: ______
Improvement: ______
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Part, Whole, or PercentβRound 2 [KEY]
Directions: Find each missing value.
1. 20% of 100 is? ππ 23. 10% of 4 is? π. π
2. 21% of 100 is? ππ 24. 20% of 4 is? π. π
3. 22% of 100 is? ππ 25. 30% of 4 is? π. π
4. 23% of 100 is? ππ 26. 50% of 4 is? π
5. 25% of 100 is? ππ 27. 25% of 4 is? π
6. 25% of 200 is? ππ 28. 75% of 4 is? π
7. 25% of 300 is? ππ 29. 80% of 4 is? π. π
8. 25% of 400 is? πππ 30. 85% of 4 is? π. π
9. 25% of 4000 is? ππππ 31. 90% of 4 is? π. π
10. 50% of 4000 is? ππππ 32. 95% of 4 is? π. π
11. 10% of 4000 is? 400 33. 5% of 4 is? π. π
12. 10% of 4700 is? πππ 34. 15% of 40 is? π
13. 10% of 4600 is? πππ 35. 15% of 30 is? π. π
14. 10% of 4630 is? πππ 36. 15% of 20 is? π
15. 10% of 463 is? ππ. π 37. 30% of 20 is? π
16. 10% of 46.3 is? π. ππ 38. 30% of 50 is? ππ
17. 10% of 18 is? π. π 39. 30% of 90 is? ππ
18. 10% of 24 is? π. π 40. 45% of 90 is? ππ. π
19. 10% of 3.63 is? π. πππ 41. 90% of 120 is? πππ
20. 10% of 0.336 is? π. ππππ 42. 125% of 40 is? ππ
21. 10% of 37 is? π. π 43. 125% of 50 is? ππ. π
22. 10% of 37.5 is? π. ππ 44. 120% of 60 is? ππ
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Percent More or LessβRound 1
Directions: Find each missing value.
1. 100% of 10 is ___? 23. 15% of 80 is ___?
2. 10% of 10 is ___? 24. 15% more than 80 is ___?
3. 10% more than 10 is ___? 25. What is 115% of 80?
4. 11 is ___% more than 10? 26. 92 is 115% of ___?
5. 11 is ___% of 10? 27. 92 is ___% more than 80?
6. 11 is 10% more than ___ ? 28. 115% of 80 is ___?
7. 110% of 10 is ___? 29. What is 15% less than 80?
8. 10% less than 10 ππ ___? 30. What % of 80 is 68?
9. 9 is ___% less than 10? 31. What % less than 80 is 68?
10. 9 is ___% of 10? 32. What % less than 80 is 56?
11. 9 is 10% less than ___? 33. What % of 80 is 56?
12. 10% of 50 is ___? 34. What is 20% more than 50?
13. 10% more than 50 is ___? 35. What is 30% more than 50?
14. 55 is ___% of 50? 36. What is 140% of 50?
15. 55 is ___% more than 50? 37. What % of 50 is 85?
16. 55 is 10% more than ___? 38. What % more than 50 is 85?
17. 110% of 50 is ___? 39. What % less than 50 is 35?
18. 10% less than 50 is ___? 40. What % of 50 is 35?
19. 45 is ___% of 50? 41. 1 is what % of 50?
20. 45 is ___% less than 50? 42. 6 is what % of 50?
21. 45 is 10% less than ___? 43. 24% of 50 is?
22. 40 is ___% less than 50? 44. 24% more than 50 is?
Number Correct: ______
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Percent More or LessβRound 1 [KEY]
Directions: Find each missing value.
1. 100% of 10 is ___? ππ 23. 15% of 80 is ___? ππ
2. 10% of 10 is ___? π 24. 15% more than 80 is ___? ππ
3. 10% more than 10 is ___? ππ 25. What is 115% of 80? ππ
4. 11 is ___% more than 10? ππ 26. 92 is 115% of ___? ππ
5. 11 is ___% of 10? πππ 27. 92 is ___% more than 80? ππ
6. 11 is 10% more than ___ ? ππ 28. 115% of 80 is ___? ππ
7. 110% of 10 is ___? ππ 29. What is 15% less than 80? ππ
8. 10% less than 10 ππ ___? π 30. What % of 80 is 68? ππ
9. 9 is ___% less than 10? ππ 31. What % less than 80 is 68? ππ
10. 9 is ___% of 10? ππ 32. What % less than 80 is 56? ππ
11. 9 is 10% less than ___? ππ 33. What % of 80 is 56? ππ
12. 10% of 50 is ___? π 34. What is 20% more than 50? ππ
13. 10% more than 50 is ___? ππ 35. What is 30% more than 50? ππ
14. 55 is ___% of 50? πππ 36. What is 140% of 50? ππ
15. 55 is ___% more than 50? ππ 37. What % of 50 is 85? πππ
16. 55 is 10% more than ___? ππ 38. What % more than 50 is 85? ππ
17. 110% of 50 is ___? ππ 39. What % less than 50 is 35? ππ
18. 10% less than 50 is ___? ππ 40. What % of 50 is 35? ππ
19. 45 is ___% of 50? ππ 41. 1 is what % of 50? π
20. 45 is ___% less than 50? ππ 42. 6 is what % of 50? ππ
21. 45 is 10% less than ___? ππ 43. 24% of 50 is? ππ
22. 40 is ___% less than 50? ππ 44. 24% more than 50 is? ππ
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Percent More or LessβRound 2
Directions: Find each missing value.
1. 100% of 20 is ___? 23. 15% of 60 is ___?
2. 10% of 20 is ___? 24. 15% more than 60 is ___?
3. 10% more than 20 is ___? 25. What is 115% of 60?
4. 22 is ___ % more than 20? 26. 69 is 115% of ___?
5. 22 is ___% of 20? 27. 69 is ___% more than 60?
6. 22 is 10% more than ___ ? 28. 115% of 60 is ___?
7. 110% of 20 is ___? 29. What is 15% less than 60?
8. 10% less than 20 is ___? 30. What % of 60 is 51?
9. 18 is ___% less than 20? 31. What % less than 60 is 51?
10. 18 is ___% of 20? 32. What % less than 60 is 42?
11. 18 is 10% less than ___? 33. What % of 60 is 42?
12. 10% of 200 is ___? 34. What is 20% more than 80?
13. 10% more than 200 is ___? 35. What is 30% more than 80?
14. 220 is ___% of 200? 36. What is 140% of 80?
15. 220 is ___% more than 200? 37. What % of 80 is 104?
16. 220 is 10% more than ___? 38. What % more than 80 is 104?
17. 110% of 200 is ___? 39. What % less than 80 is 56?
18. 10% less than 200 is ___? 40. What % of 80 is 56?
19. 180 is ___% of 200? 41. 1 is what % of 200?
20. 180 is ___% less than 200? 42. 6 is what % of 200?
21. 180 is 10% less than ___? 43. 24% of 200 is?
22. 160 is ___% less than 200? 44. 24% more than 200 is?
Number Correct: ______
Improvement: ______
6β8 Xβ’X
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Percent More or LessβRound 2 [KEY]
Directions: Find each missing value.
1. 100% of 20 is ___? ππ 23. 15% of 60 is ___? π
2. 10% of 20 is ___? π 24. 15% more than 60 is ___? ππ
3. 10% more than 20 is ___? ππ 25. What is 115% of 60? ππ
4. 22 is ___ % more than 20? ππ 26. 69 is 115% of ___? ππ
5. 22 is ___% of 20? πππ 27. 69 is ___% more than 60? ππ
6. 22 is 10% more than ___ ? ππ 28. 115% of 60 is ___? ππ
7. 110% of 20 is ___? ππ 29. What is 15% less than 60? ππ
8. 10% less than 20 is ___? ππ 30. What % of 60 is 51? ππ
9. 18 is ___% less than 20? ππ 31. What % less than 60 is 51? ππ
10. 18 is ___% of 20? ππ 32. What % less than 60 is 42? ππ
11. 18 is 10% less than ___? ππ 33. What % of 60 is 42? ππ
12. 10% of 200 is ___? ππ 34. What is 20% more than 80? ππ
13. 10% more than 200 is ___? πππ 35. What is 30% more than 80? πππ
14. 220 is ___% of 200? πππ 36. What is 140% of 80? πππ
15. 220 is ___% more than 200? ππ 37. What % of 80 is 104? πππ
16. 220 is 10% more than ___? πππ 38. What % more than 80 is 104? ππ
17. 110% of 200 is ___? πππ 39. What % less than 80 is 56? ππ
18. 10% less than 200 is ___? πππ 40. What % of 80 is 56? ππ
19. 180 is ___% of 200? ππ 41. 1 is what % of 200? π
π
20. 180 is ___% less than 200? ππ 42. 6 is what % of 200? π
21. 180 is 10% less than ___? πππ 43. 24% of 200 is? ππ
22. 160 is ___% less than 200? ππ 44. 24% more than 200 is? πππ
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Fractional PercentsβRound 1
Directions: Find the part that corresponds with each percent.
1. 1% of 100 23. 1
4% of 100
2. 1% of 200 24. 1
4% of 200
3. 1% of 400 25. 1
4% of 400
4. 1% of 800 26. 1
4% of 800
5. 1% of 1,600 27. 1
4% of 1,600
6. 1% of 3,200 28. 1
4% of 3,200
7. 1% of 5,000 29. 1
4% of 5,000
8. 1% of 10,000 30. 1
4% of 10,000
9. 1% of 20,000 31. 1
4% of 20,000
10. 1% of 40,000 32. 1
4% of 40,000
11. 1% of 80,000 33. 1
4% of 80,000
12. 1
2% of 100 34. 1% of 1,000
13. 1
2% of 200 35.
1
2% of 1,000
14. 1
2% of 400 36.
1
4% of 1,000
15. 1
2% of 800 37. 1% of 4,000
16. 1
2% of 1,600 38.
1
2% of 4,000
17. 1
2% of 3,200 39.
1
4% of 4,000
18. 1
2% of 5,000 40. 1% of 2,000
19. 1
2% of 10,000 41.
1
2% of 2,000
20. 1
2% of 20,000 42.
1
4% of 2,000
21. 1
2% of 40,000 43.
1
2% of 6,000
22. 1
2% of 80,000 44.
1
4% of 6,000
Number Correct: ______
6β8 Xβ’X
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Fractional PercentsβRound 1 [KEY]
Directions: Find the part that corresponds with each percent.
1. 1% of 100 π 23. 1
4% of 100
π
π
2. 1% of 200 π 24. 1
4% of 200
π
π
3. 1% of 400 π 25. 1
4% of 400 π
4. 1% of 800 π 26. 1
4% of 800 π
5. 1% of 1,600 ππ 27. 1
4% of 1,600 π
6. 1% of 3,200 ππ 28. 1
4% of 3,200 π
7. 1% of 5,000 ππ 29. 1
4% of 5,000 ππ
π
π
8. 1% of 10,000 πππ 30. 1
4% of 10,000 ππ
9. 1% of 20,000 πππ 31. 1
4% of 20,000 ππ
10. 1% of 40,000 πππ 32. 1
4% of 40,000 πππ
11. 1% of 80,000 πππ 33. 1
4% of 80,000 πππ
12. 1
2% of 100
π
π 34. 1% of 1,000 ππ
13. 1
2% of 200 π 35.
1
2% of 1,000 π
14. 1
2% of 400 π 36.
1
4% of 1,000 π. π
15. 1
2% of 800 π 37. 1% of 4,000 ππ
16. 1
2% of 1,600 π 38.
1
2% of 4,000 ππ
17. 1
2% of 3,200 ππ 39.
1
4% of 4,000 ππ
18. 1
2% of 5,000 ππ 40. 1% of 2,000 ππ
19. 1
2% of 10,000 ππ 41.
1
2% of 2,000 ππ
20. 1
2% of 20,000 πππ 42.
1
4% of 2,000 π
21. 1
2% of 40,000 πππ 43.
1
2% of 6,000 ππ
22. 1
2% of 80,000 πππ 44.
1
4% of 6,000 ππ
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Fractional PercentsβRound 2
Directions: Find the part that corresponds with each percent.
1. 10% of 30 23. 101
2% of 100
2. 10% of 60 24. 101
2% of 200
3. 10% of 90 25. 101
2% of 400
4. 10% of 120 26. 101
2% of 800
5. 10% of 150 27. 101
2% of 1,600
6. 10% of 180 28. 101
2% of 3,200
7. 10% of 210 29. 101
2% of 6,400
8. 20% of 30 30. 101
4% of 400
9. 20% of 60 31. 101
4% of 800
10. 20% of 90 32. 101
4% of 1,600
11. 20% of 120 33. 101
4% of 3,200
12. 5% of 50 34. 10% of 1,000
13. 5% of 100 35. 101
2% of 1,000
14. 5% of 200 36. 101
4% of 1,000
15. 5% of 400 37. 10% of 2,000
16. 5% of 800 38. 101
2% of 2,000
17. 5% of 1,600 39. 101
4% of 2,000
18. 5% of 3,200 40. 10% of 4,000
19. 5% of 6,400 41. 101
2% of 4,000
20. 5% of 600 42. 101
4% of 4,000
21. 10% of 600 43. 10% of 5,000
22. 20% of 600 44. 101
2% of 5,000
Number Correct: ______
Improvement: ______
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Fractional PercentsβRound 2 [KEY]
Directions: Find the part that corresponds with each percent.
1. 10% of 30 π 23. 101
2% of 100 ππ. π
2. 10% of 60 π 24. 101
2% of 200 ππ
3. 10% of 90 π 25. 101
2% of 400 ππ
4. 10% of 120 ππ 26. 101
2% of 800 ππ
5. 10% of 150 ππ 27. 101
2% of 1,600 πππ
6. 10% of 180 ππ 28. 101
2% of 3,200 πππ
7. 10% of 210 ππ 29. 101
2% of 6,400 πππ
8. 20% of 30 π 30. 101
4% of 400 ππ
9. 20% of 60 ππ 31. 101
4% of 800 ππ
10. 20% of 90 ππ 32. 101
4% of 1,600 πππ
11. 20% of 120 ππ 33. 101
4% of 3,200 πππ
12. 5% of 50 π. π 34. 10% of 1,000 πππ
13. 5% of 100 π 35. 101
2% of 1,000 πππ
14. 5% of 200 ππ 36. 101
4% of 1,000 πππ. π
15. 5% of 400 ππ 37. 10% of 2,000 πππ
16. 5% of 800 ππ 38. 101
2% of 2,000 πππ
17. 5% of 1,600 ππ 39. 101
4% of 2,000 πππ
18. 5% of 3,200 πππ 40. 10% of 4,000 πππ
19. 5% of 6,400 πππ 41. 101
2% of 4,000 πππ
20. 5% of 600 ππ 42. 101
4% of 4,000 πππ
21. 10% of 600 ππ 43. 10% of 5,000 πππ
22. 20% of 600 ππ0 44. 101
2% of 5,000 πππ
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Applying Properties of Exponents to Generate Equivalent Expressions IβRound 1
Directions: Simplify each expression using the laws of exponents. Use the least number of bases possible and only
positive exponents. All letters denote numbers.
1. 22 β 23 23. 63 β 62
2. 22 β 24 24. 62 β 63
3. 22 β 25 25. (β8)3 β (β8)7
4. 37 β 31 26. (β8)7 β (β8)3
5. 38 β 31 27. (0.2)3 β (0.2)7
6. 39 β 31 28. (0.2)7 β (0.2)3
7. 76 β 72 29. (β2)12 β (β2)1
8. 76 β 73 30. (β2.7)12 β (β2.7)1
9. 76 β 74 31. 1.16 β 1.19
10. 1115 β 11 32. 576 β 579
11. 1116 β 11 33. π₯6 β π₯9
12. 212 β 22 34. 27 β 4
13. 212 β 24 35. 27 β 42
14. 212 β 26 36. 27 β 16
15. 995 β 992 37. 16 β 43
16. 996 β 993 38. 32 β 9
17. 997 β 994 39. 32 β 27
18. 58 β 52 40. 32 β 81
19. 68 β 62 41. 54 β 25
20. 78 β 72 42. 54 β 125
21. π8 β π2 43. 8 β 29
22. π 8 β π 2 44. 16 β 29
Number Correct: ______
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Applying Properties of Exponents to Generate Equivalent Expressions IβRound 1 [KEY]
Directions: Simplify each expression using the laws of exponents. Use the least number of bases possible and only
positive exponents. All letters denote numbers.
1. 22 β 23
ππ 23. 63 β 62 ππ
2. 22 β 24 ππ 24. 62 β 63 ππ
3. 22 β 25 ππ 25. (β8)3 β (β8)7 (βπ)ππ
4. 37 β 31 ππ 26. (β8)7 β (β8)3 (βπ)ππ
5. 38 β 31 ππ 27. (0.2)3 β (0.2)7 (π. π)ππ
6. 39 β 31 πππ 28. (0.2)7 β (0.2)3 (π. π)ππ
7. 76 β 72 ππ 29. (β2)12 β (β2)1 (βπ)ππ
8. 76 β 73 ππ 30. (β2.7)12 β (β2.7)1 (βπ. π)ππ
9. 76 β 74 πππ 31. 1.16 β 1.19 π. πππ
10. 1115 β 11 ππππ 32. 576 β 579 ππππ
11. 1116 β 11 ππππ 33. π₯6 β π₯9 πππ
12. 212 β 22 πππ 34. 27 β 4 ππ
13. 212 β 24 πππ 35. 27 β 42 πππ
14. 212 β 26 πππ 36. 27 β 16 πππ
15. 995 β 992 πππ 37. 16 β 43 ππ
16. 996 β 993 πππ 38. 32 β 9 ππ
17. 997 β 994 ππππ 39. 32 β 27 ππ
18. 58 β 52 πππ 40. 32 β 81 ππ
19. 68 β 62 πππ 41. 54 β 25 ππ
20. 78 β 72 πππ 42. 54 β 125 ππ
21. π8 β π2 πππ 43. 8 β 29 πππ
22. π 8 β π 2 πππ 44. 16 β 29 πππ
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Applying Properties of Exponents to Generate Equivalent Expressions IβRound 2
Directions: Simplify each expression using the laws of exponents. Use the least number of bases possible and only
positive exponents. All letters denote numbers.
1. 52 β 53 23. 73 β 72
2. 52 β 54 24. 72 β 73
3. 52 β 55 25. (β4)3 β (β4)11
4. 27 β 21 26. (β4)11 β (β4)3
5. 28 β 21 27. (0.2)3 β (0.2)11
6. 29 β 21 28. (0.2)11 β (0.2)3
7. 36 β 32 29. (β2)9 β (β2)5
8. 36 β 33 30. (β2.7)5 β (β2.7)9
9. 36 β 34 31. 3.16 β 3.16
10. 715 β 7 32. 576 β 576
11. 716 β 7 33. π§6 β π§6
12. 1112 β 112 34. 4 β 29
13. 1112 β 114 35. 42 β 29
14. 1112 β 116 36. 16 β 29
15. 235 β 232 37. 16 β 43
16. 236 β 233 38. 9 β 35
17. 237 β 234 39. 35 β 9
18. 137 β 133 40. 35 β 27
19. 157 β 153 41. 57 β 25
20. 177 β 173 42. 57 β 125
21. π₯7 β π₯3 43. 211 β 4
22. π¦7 β π¦3 44. 211 β 16
Number Correct: ______
Improvement: ______
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Applying Properties of Exponents to Generate Equivalent Expressions IβRound 2 [KEY]
Directions: Simplify each expression using the laws of exponents. Use the least number of bases possible and only
positive exponents. All letters denote numbers.
1. 52 β 53 ππ 23. 73 β 72 ππ
2. 52 β 54 ππ 24. 72 β 73 ππ
3. 52 β 55 ππ 25. (β4)3 β (β4)11 (βπ)ππ
4. 27 β 21 ππ 26. (β4)11 β (β4)3 (βπ)ππ
5. 28 β 21 ππ 27. (0.2)3 β (0.2)11 (π. π)ππ
6. 29 β 21 πππ 28. (0.2)11 β (0.2)3 (π. π)ππ
7. 36 β 32 ππ 29. (β2)9 β (β2)5 (βπ)ππ
8. 36 β 33 ππ 30. (β2.7)5 β (β2.7)9 (βπ. π)ππ
9. 36 β 3 πππ 31. 3.16 β 3.16 π. πππ
10. 715 β 7 πππ 32. 576 β 576 ππππ
11. 716 β 7
πππ 33. π§6 β π§6 πππ
12. 1112 β 112 ππππ 34. 4 β 29 πππ
13. 1112 β 114 ππππ 35. 42 β 29 πππ
14. 1112 β 116 ππππ 36. 16 β 29 πππ
15. 235 β 232 πππ 37. 16 β 43 ππ
16. 236 β 233 πππ 38. 9 β 35 ππ
17. 237 β 234 ππππ 39. 35 β 9 ππ
18. 137 β 133 ππππ 40. 35 β 27 ππ
19. 157 β 153 ππππ 41. 57 β 25 ππ
20. 177 β 173 ππππ 42. 57 β 125 πππ
21. π₯7 β π₯3 πππ 43. 211 β 4 πππ
22. π¦7 β π¦3 πππ 44. 211 β 16 πππ
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Applying Properties of Exponents to Generate Equivalent Expressions IIβRound 1
Directions: Simplify each expression using the laws of exponents. Use the least number of bases possible and only positive
exponents. When appropriate, express answers without parentheses or as equal to 1. All letters denote numbers.
1. 45 β 4β4 23. (12
)6
2. 45 β 4β3 24. (3π₯)5
3. 45 β 4β2 25. (3π₯)7
4. 7β4 β 711 26. (3π₯)9
5. 7β4 β 710 27. (8β2)3
6. 7β4 β 79 28. (8β3)3
7. 9β4 β 9β3 29. (8β4)3
8. 9β4 β 9β2 30. (220)50
9. 9β4 β 9β1 31. (220)55
10. 9β4 β 90 32. (220)60
11. 50 β 51 33. (1
11)
β5
12. 50 β 52 34. (1
11)
β6
13. 50 β 53 35. (1
11)
β7
14. (123)9 36. 56β23
56β34
15. (123)10 37. 87β12
87β34
16. (123)11 38. 23β15
23β17
17. (7β3)β8 39. (β2)β12 β (β2)1
18. (7β3)β9 40. 2π¦
π¦3
19. (7β3)β10 41. 5π₯π¦7
15π₯7π¦
20. (12
)9
42. 16π₯6π¦9
8π₯β5π¦β11
21. (12
)8
43. (23 β 4)β5
22. (12
)7
44. (9β8)(27β2)
Number Correct: ______
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Applying Properties of Exponents to Generate Equivalent Expressions IIβRound 1 [KEY]
Directions: Simplify each expression using the laws of exponents. Use the least number of bases possible and only positive
exponents. When appropriate, express answers without parentheses or as equal to 1. All letters denote numbers.
1. 45 β 4β4 ππ 23. (12
)6
π
ππ
2. 45 β 4β3 ππ 24. (3π₯)5 ππππ
3. 45 β 4β2 ππ 25. (3π₯)7 ππππ
4. 7β4 β 711 ππ 26. (3π₯)9 ππππ
5. 7β4 β 710 ππ 27. (8β2)3 π
ππ
6. 7β4 β 79 ππ 28. (8β3)3 π
ππ
7. 9β4 β 9β3 π
ππ 29. (8β4)3
π
πππ
8. 9β4 β 9β2 π
ππ 30. (220)50 π
9. 9β4 β 9β1 π
ππ 31. (220)55 π
10. 9β4 β 90 π
ππ 32. (220)60 π
11. 50 β 51 ππ 33. (1
11)
β5
πππ
12. 50 β 52 ππ 34. (1
11)
β6
πππ
13. 50 β 53 ππ 35. (1
11)
β7
πππ
14. (123)9 ππππ 36. 56β23
56β34 ππππ
15. (123)10 ππππ 37. 87β12
87β34 ππππ
16. (123)11 ππππ 38. 23β15
23β17 πππ
17. (7β3)β8 πππ 39. (β2)β12 β (β2)1 π
(βπ)ππ
18. (7β3)β9 πππ 40. 2π¦
π¦3
π
ππ
19. (7β3)β10 πππ 41. 5π₯π¦7
15π₯7π¦
ππ
πππ
20. (12
)9
π
ππ 42.
16π₯6π¦9
8π₯β5π¦β11 πππππππ
21. (12
)8
π
ππ 43. (23 β 4)β5
π
πππ
22. (12
)7
π
ππ 44. (9β8)(27β2)
π
πππ
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Applying Properties of Exponents to Generate Equivalent Expressions IIβRound 2
Directions: Simplify each expression using the laws of exponents. Use the least number of bases possible and only positive
exponents. When appropriate, express answers without parentheses or as equal to 1. All letters denote numbers.
1. 115 β 11β4 23. (37
)5
2. 115 β 11β3 24. (18π₯π¦)5
3. 115 β 11β2 25. (18π₯π¦)7
4. 7β7 β 79 26. (18π₯π¦)9
5. 7β8 β 79 27. (5.2β2)3
6. 7β9 β 79 28. (5.2β3)3
7. (β6)β4 β (β6)β3 29. (5.2β4)3
8. (β6)β4 β (β6)β2 30. (226)0
9. (β6)β4 β (β6)β1 31. (2212)0
10. (β6)β4 β (β6)0 32. (2218)0
11. π₯0 β π₯1 33. (45
)β5
12. π₯0 β π₯2 34. (45
)β6
13. π₯0 β π₯3 35. (45
)β7
14. (125)9 36. (6β2
75 )
β11
15. (126)9 37. (6β2
75 )
β12
16. (127)9 38. (6β2
75 )
β13
17. (7β3)β4 39. (6β2
75 )
β15
18. (7β4)β4 40. 42ππ10
14πβ9π
19. (7β5)β4 41. 5π₯π¦7
25π₯7π¦
20. (37
)8
42. 22π15π32
121ππβ5
21. (37
)7
43. (7β8 β 49)β5
22. (37
)6
44. (369)(216β2)
Number Correct: ______
Improvement: ______
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Applying Properties of Exponents to Generate Equivalent Expressions IIβRound 2 [KEY]
Directions: Simplify each expression using the laws of exponents. Use the least number of bases possible and only positive
exponents. When appropriate, express answers without parentheses or as equal to 1. All letters denote numbers.
1. 115 β 11β4 πππ 23. (37
)5
ππ
ππ
2. 115 β 11β3 πππ 24. (18π₯π¦)5 πππππππ
3. 115 β 11β2 πππ 25. (18π₯π¦)7 πππππππ
4. 7β7 β 79 ππ 26. (18π₯π¦)9 πππππππ
5. 7β8 β 79 ππ 27. (5.2β2)3 π
(π. π)π
6. 7β9 β 79 π 28. (5.2β3)3 π
(π. π)π
7. (β6)β4 β (β6)β3 π
(βπ)π 29. (5.2β4)3
π
(π. π)ππ
8. (β6)β4 β (β6)β2 π
(βπ)π 30. (226)0 π
9. (β6)β4 β (β6)β1 π
(βπ)π 31. (2212)0 π
10. (β6)β4 β (β6)0 π
(βπ)π 32. (2218)0 π
11. π₯0 β π₯1 ππ 33. (45
)β5
ππ
ππ
12. π₯0 β π₯2 ππ 34. (45
)β6
ππ
ππ
13. π₯0 β π₯3 ππ 35. (45
)β7
ππ
ππ
14. (125)9 ππππ 36. (6
β2
75 )
β11
ππππππ
15. (126)9 ππππ 37. (6
β2
75 )
β12
ππππππ
16. (127)9 ππππ 38. (6
β2
75 )
β13
ππππππ
17. (7β3)β4 πππ 39. (6
β2
75 )
β15
ππππππ
18. (7β4)β4 πππ 40. 42ππ10
14πβ9π ππππππ
19. (7β5)β4 πππ 41. 5π₯π¦7
25π₯7π¦
ππ
πππ
20. (37
)8
ππ
ππ 42.
22π15π32
121ππβ5
πππππππ
ππ
21. (37
)7
ππ
ππ 43. (7β8 β 49)β5 πππ
22. (37
)6
ππ
ππ 44. (369)(216β2)
πππ
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Operations with Numbers Expressed in Scientific Notation I
1. (5 Γ 104)2
π. π Γ πππ
2. (2 Γ 109)4
π. π Γ ππππ
3. (1.2Γ104)+(2Γ104)+(2.8Γ104)
3=
π Γ πππ
4. 7Γ1015
14Γ109
π Γ πππ
5. 4Γ102
2Γ108
π Γ ππβπ
6. (7Γ109)+(6Γ109)
2
π. π Γ πππ
7. (9 Γ 10β4)2
π. π Γ ππβπ
8. (9.3 Γ 1010) β (9 Γ 1010)
π Γ πππ
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Operations With Numbers Expressed in Scientific Notation II
1. 3Γ108
5Γ104
π Γ πππ
2. (6 Γ 10β5)(7 Γ 1011)
π. π Γ πππ
3. (3.2 Γ 10β5) + (6.7 Γ 10β5) + (5.1 Γ 10β5)
π. π Γ ππβπ
4. (6 Γ 10β3)2
π. π Γ ππβπ
5. (6Γ103)+(8Γ103)+(2Γ103)
4
π Γ πππ
6. (6.1 Γ 105) β (6 Γ 105)
π Γ πππ
7. 9Γ103
4.5Γ1015
π Γ ππππ
8. (4 Γ 105)3
π. π Γ ππππ
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Multistep Equations I
Set 1:
3π₯ + 2 = 5π₯ + 6
4(5π₯ + 6) = 4(3π₯ + 2)
3π₯ + 2
6=
5π₯ + 6
6
Answer for each problem in this set is π = βπ.
Set 2:
6 β 4π₯ = 10π₯ + 9
β2(β4π₯ + 6) = β2(10π₯ + 9)
10π₯ + 9
5=
6 β 4π₯
5
Answer for each problem in this set is π = βπ
ππ.
Set 3:
5π₯ + 2 = 9π₯ β 18
8π₯ + 2 β 3π₯ = 7π₯ β 18 + 2π₯
2 + 5π₯
3=
7π₯ β 18 + 2π₯
3
Answer for each problem in this set is π = π.
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Multistep Equations II
1. 2(π₯ + 5) = 3(π₯ + 6)
π = βπ
2. 3(π₯ + 5) = 4(π₯ + 6)
π = βπ
3. 4(π₯ + 5) = 5(π₯ + 6)
π = βππ
4. β(4π₯ + 1) = 3(2π₯ β 1)
π =π
π
5. 3(4π₯ + 1) = β(2π₯ β 1)
π = βπ
π
6. β3(4π₯ + 1) = 2π₯ β 1
π = βπ
π
7. 15π₯ β 12 = 9π₯ β 6
π = π
8. 13
(15π₯ β 12) = 9π₯ β 6
π =π
π
9. 23
(15π₯ β 12) = 9π₯ β 6
π = π
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Multistep Equations III
1. 2.5π₯ β 14.8 = 26.7
π = ππ. π
2. 3
4(8π₯ β 12) =
1
5(10π₯ + 15)
π = π
3. β1
5(2π₯ β 3) =
1
2(4 β 3π₯)
π =ππ
ππ= π
π
ππ
4. 3.1(2π₯ β 13.4) = 3.8π₯ β 14.7 + 2.3π₯
π = πππ. π
5. 2
3π₯ β
4
5+
1
3π₯ = 3π₯ β
3
5
π = βπ
ππ
6. 4(2.4π₯ β 4.6) = β(2.2 β 3.6π₯)
π = π. π
7. 4(5.9 + 0.8π₯) = 2(29.5 β 4.3π₯)
π = π
8. 1
4(
2
3π₯ + 4) =
3
4(
1
3β
2
3π₯)
π = βπ
π= βπ
π
π
9. 6.5(2.6π₯ + 7.8) = β5.2(β6.5 β 2.6π₯) + 3.9π₯
π = ππ. π
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Area and Volume I
1. Find the area of the square shown below.
π¨ = (π π)π = ππ ππ
2. Find the volume of the cube shown below.
π½ = (π π)π = ππ ππ
3. Find the area of the rectangle shown below.
π¨ = (π ππ)(π ππ)
= ππ πππ
4. Find the volume of the rectangular prism shown below.
π½ = (ππ πππ)(π ππ) = πππ πππ
5. Find the area of the circle shown below.
π¨ = (π π)ππ = πππ ππ
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6. Find the volume of the cylinder shown below.
π½ = (πππ ππ)(ππ π) = ππππ ππ
7. Find the area of the circle shown below.
π¨ = (π ππ.)ππ = πππ πππ
8. Find the volume of the cone shown below.
π½ = (π
π) (πππ πππ)(ππ ππ.)
= ππππ πππ
9. Find the area of the circle shown below.
π¨ = (π ππ)ππ
= πππ πππ
10. Find the volume of the sphere shown below.
π½ = (π
π) π (ππ πππ)(π ππ)
=ππππ
ππ πππ
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Area and Volume II
1. Find the area of the square shown below.
π¨ = (π ππ)π
= ππ πππ
2. Find the volume of the cube shown below.
π½ = (π ππ)π
= πππ πππ
3. Find the area of the rectangle shown below.
π¨ = (π π)(π π)
= ππ ππ
4. Find the volume of the rectangular prism show below.
π½ = (ππ ππ)(π π)
= πππ ππ
5. Find the area of the circle shown below.
π¨ = (π π)ππ
= πππ ππ
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6. Find the volume of the cylinder show below.
π½ = (πππ ππ)(ππ π)
= ππππ ππ
7. Find the area of the circle shown below.
π¨ = (π ππ.)ππ
= πππ πππ
8. Find the volume of the cone show below.
π½ = (π
π) (πππ πππ)(ππ ππ.)
= ππππ πππ
9. Find the area of the circle shown below.
π¨ = (π ππ)ππ
= πππ πππ
10. Find the volume of the sphere shown below.
π½ = (π
π) π (π ππ)π
=πππ ππ
ππ
= ππππ πππ